H C VERMA Solutions for Class 12-science Physics Chapter 6 - Heat Transfer

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Chapter 6 - Heat Transfer Exercise 98

Question 1

A uniform slab of dimension 10cm×10cm×1cm is kept between two heat reservoirs at temperatures 10°C and 90°C The larger surface areas touches the reservoirs. The thermal conductivity of the material is 0.08 W/m-°C Find the amount of heat flowing through the slab per minute.

Solution 1

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 2

A liquid-nitrogen container is made of a 1cm thick thermocoal sheet having thermal conductivity 0.025 J/m-s-°C Liquid nitrogen at 80K is kept in it. A total area of 0.80m2 is in contact with the liquid nitrogen. The atmospheric temperature is 300K. Calculate the rate of heat flow from the atmosphere to the liquid nitrogen.

Solution 2

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

= 440W

Question 3

The normal body - temperature of a person is 97°F Calculate the rate at which heat is flowing out of his body through the clothes assuming the following values. Room temperature = 47°F surface of the body under clothes = 1.6m2 conductivity of the cloth = 0.04 J/m-s-°C, thickness of the cloth = 0.5cm.

Solution 3

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 4

Water is boiled in a container having a bottom of surface area225cm2, thickness 1.0mm and thermal conductivity 50W/m-°C 100g of water is converted into steam per minute in the steady state after the boiling starts. Assuming that no heat is lost to the atmosphere, calculate the temperature of the lower surface of the bottom. Latent heat of vaporization of water = 2.26×106 J/kg.

Solution 4

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Also Rate of conversion = H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 5

One end of a steel rod (K=46 J/m-s-°C.) of length of 1.0m is kept in ice at 0°C and the other end is kept in boiling water at 100°C The area of cross - section of the rod is 0.04 cm2. Assuming no heat loss to the atmosphere, find the mass of the ice melting per second. Latent heat of fusion of ice = 3.36×106 J/kg.

Solution 5

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 6

An ice box almost completely filled with ice at 0°C is dipped into a large volume of water at 20°C. The box has walls of surface area 2400cm2 thickness 2.0mm and thermal conductivity 0.06W/m-°C Calculate the rate at which the ice melts in the box. Latent heat of fusion of ice = 3.4×105 J/kg

Solution 6

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Ice melt at rate of m/t which is:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 7

A pitcher with 1mm thick porous walls contains 10kg of water. Water comes to its outer surface and evaporates at the rate of 0.1 g/s. The surface area of the pitcher (one side) = 200cm2 The room temperature = 42°C, latent heat of vaporization = 2.27×106 J/kg and the thermal conductivity of the porous walls = 0.80 J/m-s-°C Calculate the temperature of water in the pitcher when it attains a constant value.

Solution 7

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Also

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 8

A steel frame (K = 45W/m-°C) of total length 60cm and cross - sectional area 0.20cm2 forms three sides of a square. The free ends are maintained at 20°C and 40°C. Find the rate of heat flow through a cross - section of the frame.

Solution 8

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 9

Water at 50°C is filled in a closed cylindrical vessel of height 10cm and cross - sectional area 10cm2. The walls of the vessel are adiabatic but the flat parts are made of 1mm thick Aluminium (K=200 J/m-s-°C). Assume that the outside temperature is 20°C. The density of water is 1000 kg/m3, and the specific heat capacity of water = 4200 J/kg-°C. Estimate the time taken for the temperature to fall by 1.0°C. Make any simplifying assumptions you need but specify them.

Solution 9

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

= 6000

Heat goes out from two surfaces, Hence net heat flow is:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

= 12000

Also,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 10

The left end of a copper rod (length = 20cm, area of cross - section =0.20cm2) is maintained at 20°C and the right end is maintained at 80°C. Neglecting any loss of heat through radiation, find (a) the temperature at a point 11cm from the left end and (b) the heat current through the rod. Thermal conductivity of copper = 385 W/m-°C.

Solution 10

(a) We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer________(1)

Also,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

(b) From equation (1) heat flow,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Chapter 6 - Heat Transfer Exercise 99

Question 11

The ends of a metre stick are maintained at H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer and 0°CH-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer One end of a rod is maintained at 25°C Where should its other end be touched on the metre stick so that there is no heat current in the rod in steady state?

Solution 11

Let the point touched be 0. As no heat is flowing

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

x is distance between 0°C end and point which is touched.

Question 12

A cubical box of volume 216cm3 is made up of 0.1cm thick wood. The inside is heated electrically by a 100W heater. It is found that the temperature difference between the inside and the outside surface is 5°C in steady state. Assuming that the entire electrical energy spent appears as heat, find the thermal conductivity of the material of the box.

Solution 12

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 13

Figure shows water in a container having 2.0 mm thick walls made of a material of thermal conductivity 0.50 W/m-°C The container is kept in a melting ice bath at 0°C The total surface area in contact with water is 0.05m2 A wheel is clamped inside the water and is coupled to a block of mass M as shown in the figure. As the block goes down, the wheel rotates. It is found that after some time a steady state is reached in which the block goes down with a constant speed of 10 cm/s and the temperature of the water remains constant at 1.0°C Find the mass M of the block. Assume that the heat flows out of the water only through the walls in contact. Take g=10 m/s2.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer

 

Solution 13

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 14

On a winter day when the atmospheric temperature drops to -10°C, ice forms on the surface of a lake. (a) Calculate the rate of increase of thickness of the ice when 10cm of ice is already formed. (b) Calculate the total time taken in forming 10cm of ice. Assume that the temperature of the entire water reaches 0°C before the ice starts forming. Density of water = 1000 kg/m3 latent heat of fusion of ice = 3.36×105 J/kg and thermal conductivity of ice = 1.7 W/m-°C Neglect the expansion of water on freezing.

Solution 14

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Rearranging

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer(As Q = mL)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

(b) Now, we consider a small ship of ice.

And,  H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Or H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

OrH-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Integrating

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 15

Consider the situation of the previous problem. Assume that the temperature of the water at the bottom of the lake remains constant at 4°C as the ice forms on the surface (the heat required to maintain the temperature of the bottom layer may come from the bed of the lake). The depth of the lake is 1.0m. Show that the thickness of the ice formed attains a steady state maximum value. Find this value. The thermal conductivity of water = 0.50 W/m-°C Take other relevant data from the previous problem.

Solution 15

Heat conducted at point above which ice cannot be formed is same from both levels. Thus,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 16

Three rods of lengths 20cm each and area of cross - section 1cm2 are joined to form a triangle ABC. The conductivities of the rods are KAC = 50 J/m-s-°C, KBC = 200 J/m-s-°C and KAC = 400 J/m-s- °C. Then H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transferjunctions A, B and C are maintained at 40°C, 80°C and 80°C respectively. Find the rate of heat flowing through the rods AB, AC and BC.

Solution 16

(a) We know

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

(b) H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

(c) H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 17

A semicircular rod is joined at its end to a straight rod of the same material and the same cross - sectional area. The straight rod forms a diameter of the other rod. The junctions are maintained at different temperatures. Find the ratio of the heat transferred through a cross - section of the semicircular rod to the heat transferred through a cross - section of the straight rod in a given time.

Solution 17

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

AndH-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Taking ratio we get

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 18

A metal rod of cross - sectional area 10cm2 is being heated at one end. At one time, the temperature gradient is 5.0H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer/cm at cross - section A and is 2.5°C /cm at cross - section B. Calculate the rate at which the temperature is increasing in the part AB = 0.40J/°C, thermal conductivity of the material of the rod = 200 W/m-°C. Neglect any loss of heat to the atmosphere.

Solution 18

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

And H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Net H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Also, H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 19

Steam at 120°C is continuously passed through a 50cm long rubber tube of inner and outer radii 1.0cm and 1.2cm. The room temperature is 30°C. Calculate the rate of heat flow through the walls of the tube. Thermal conductivity of rubber = 0.15 J/m-s-°C.

Solution 19

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 20

A hole of radius r1 is made centrally in a uniform circular disc of thickness d and radius r2. The inner surface (a cylinder of length d and radius r1) is maintained at a temperature θ1 and the outer surface (a cylinder of length d and radius r2) is maintained at a temperature θ2(θ1 > θ2). The thermal conductivity of the material of the disc is K. Calculate the heat flowing per unit time through the disc.

Solution 20

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Now let H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 21

A hollow tube has a length L, inner radius R1 and the outer radius R2. The material has a thermal conductivity K. Find the heat flowing through the walls of the tube if (a) the flat ends are maintained at temperature T1 and T2 (T1 > T2) and the inside of the tube is maintained at temperature H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer and the outside is maintained at T2.

Solution 21

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Cylinders are concentric and heat flow through them is:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Rearranging and integrating

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 22

A composite slab is prepared by pasting two plates of thicknesses L1 and L2 and thermal conductivity K1 and K2. The slabs have equal cross - sectional area. Find the equivalent conductivity of the slab.

Solution 22

In this case thermal conductivities are in series with each other. Thus,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Solving we get

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 23

Figure shows a copper rod joined to a steel rod. The rods have equal length and equal cross - sectional area. The free end of the copper rod is kept at 0°C and that of the steel rod is kept at 100°C Find the temperature at the junction of the rods. Conductivity of copper = 390 W/m - °C and that of steel = 46 W/m - °C.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer

 

Solution 23

Both elements are in series with each other. Thus,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 24

An aluminium rod and a copper rod of equal length 1.0m and cross - sectional area 1cm2 are welded together as shown in figure. One end is kept at a temperature of 20°C and the other at 60°C. Calculate the amount of heat taken out per second from the hot end. Thermal conductivity of aluminium = 200 W/m - °C and of copper = 390 W/m -°C.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer

 

 

Solution 24

Since rod of the both elements are joined in parallel. Thus,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Also,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Chapter 6 - Heat Transfer Exercise 100

Question 25

Figure shows an aluminium rod joined to a copper rod. Each of the rods has a length of 20cm and area of cross - section 0.20cm2. The junction is maintained at a constant temperature 40°C and the two ends are maintained at 80°C Calculate the amount of heat taken out from the cold junction in one minute after the steady state is reached. The conductivities are H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer = 200 W/m - °C and Kcu = 400 W/m - °C.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

 

Solution 25

Net heat per second is given as:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer + H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Heat drawn per minute is

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 26

Consider the situation shown in figure. The frame is made of the same material and has a uniform cross - sectional area everywhere. Calculate the amount of heat flowing per second through a cross - section of the bent part if the total heat taken out per second from the end at 100°C is 130 J.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

 

Solution 26

According to Question

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Also,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

And,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Taking ratio, we get

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer = H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer = H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer________(2)

Substituting equation (2) in (1) we get

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 27

Suppose the bent part of the frame of the previous problem has a thermal conductivity of 780 J/m-s-°C whereas it is 390 J/m-s-°C for the straight part. Calculate the ratio of the rate of heat flow through the bent part to the rate of heat flow through the straight part.

Solution 27

For bent part,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

For straight part,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Dividing (1) and (2) we get,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 28

A room has a window fitted with a single 1.0m × 2.0m glass of thickness 2mm. (a) Calculate the rate of heat flow through the closed window when the temperature inside the room is 32°C and that outside is 40°C (b) The glass is now replaced by two glasspanes, each having a thickness of 1mm and separated by a distance of 1mm. Calculate the rate of heat flow under the same conditions of temperature. Thermal conductivity of window glass = 1.0 J/m-s-°C and that of air = 0.025 J/m-s-°C

Solution 28

(a) We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

= H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

(b) Resistance by glass is, H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

And resistance by air is H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 29

The two rods shown in figure have identical geometrical dimensions. They are in contact with two heat baths at temperatures 100°C and 0°C The temperature of the junction is 70°CH-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer Find the temperature of the junction if the rods are interchanged.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Solution 29

For case I:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

And

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Here

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

For case II:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

And

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Here

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 30

The three rods shown in figure have identical geometrical dimensions. Heat flows from the hot end at a rate of 40W in the arrangement (a). Find the rates of heat flow when the rods are joined as in arrangement (b) and in (c). Thermal conductivities of aluminium and copper are 200 W/m -°C and 400 W/m -°CH-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer respectively.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

 

Solution 30

Net Resistance is:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Also,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

(b) Now,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

= H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

= H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Also,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

(c) H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Also,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 31

Four identical rods AB, CD, CF and DE are joined as shown in figure. The length, cross - sectional area and thermal conductivity of each rod are l, A and K respectively. The ends A, E and F are maintained at temperatures T1, T2 and T3 respectively. Assuming no loss of heat to the atmosphere, find the temperature at B.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Solution 31

According to Question,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 32

Seven rods A, B, C, D, E, F and G are joined as shown in figure. All the rods have equal cross - sectional area A and the length l. The thermal conductivities of the rods are KA= KC= K0, KB= KD= 2K0, KE= 3K0, KF= 4K0 and KG= 5K0.The rod E is kept at a constant temperature T1 and the rod G is kept at a constant temperature T2(T2 > T1) (a) Show that the rod F has a uniform temperature H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer (b) Find the rate of heat flow from the source which maintains the temperatureH-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer

 

 

 

Solution 32

In bar F, temperature at both ends is same:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

As

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 33

Find the rate of heat flow through a cross - section of the rod shown in figure (θ2 > θ1) Thermal conductivity of the material of the rod is K.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

 

Solution 33

We Know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

And

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Simplifying and differentiating w.r.t 'x'

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer - 0

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Also,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Integrating

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Chapter 6 - Heat Transfer Exercise 101

Question 34

A rod of negligible heat capacity has length 20cm, area of cross - section 1.0cm2 and thermal conductivity 200 W/m -°C The temperature of one end is maintained at 0°C and that of the other end is slowly and linearly varied from 0°C to 60°C in 10 minutes. Assuming no loss of heat through the sides, find the total heat transmitted through the rod in these 10 minutes.

Solution 34

We Know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Also,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Solving we get

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 35

A hollow metallic sphere of radius 20cm surrounds a concentric metallic sphere of radius 5cm. The space between the two spheres is filled with a nonmetallic material. The inner and outer spheres are maintained at 50°C and 10°C respectively and it is found that 100 J of heat passes from the inner sphere to the outer sphere per second. Find the thermal conductivity of the material between the spheres.

Solution 35

For small strip having thickness 'dr', we have,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Rearranging and integrating we get,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

 

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Solving we get

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 36

Figure shows two adiabatic vessels, each containing a mass m of water at different temperatures. The ends of a metal rod of length L, area of cross - section A and thermal conductivity K, are inserted in the water as shown in the figure. Find the time taken for the difference between the temperatures in the vessels to become half of the original value. The specific heat capacity of water is S. Neglect the heat capacity of the rod and the container and any loss of heat to the atmosphere.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Solution 36

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Rise in temperature is : H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

And Fall in temperature is : H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Also, Final temperatures are given as :

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

And

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Now, net temperature is

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

= H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Rearranging and integrating we get

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 37

Two bodies of masses H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer and specific heat capacities s1 and s2 are connected by a rod of length l, cross-sectional area A, thermal conductivity K and negligible heat capacity. The whole system is thermally insulated. At time t = 0, the temperature of the first body is H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transferand the temperature of the second body is T2 (T2> T1) Find the temperature difference between the two bodies at time t.

Solution 37

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Rise in temperature is : H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

And Fall in temperature is : H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Final temperature are given as:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

And

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

And also,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Solving we get

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Integrating we get

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 38

An amount n (in moles) of a monatomic gas at an initial temperature H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer is enclosed in a cylindrical vessel fitted with a light piston. The surrounding air has a temperature H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer and the atmospheric pressure is H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer. Heat may be conducted between the surrounding and the gas through the bottom of the cylinder. The bottom has a surface area A, thickness H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer and thermal conductivity K. Assuming all changes to be slow, find the distance moved by the piston in time t.

Solution 38

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Also 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Integrating and solving we get

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

And H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 39

Assume that the total surface area of a human body is 1.6cm2 and that it radiates like an ideal radiator. Calculate the amount of energy radiated per second by the body if the body temperature is 37°C. Stefan constantH-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer.

Solution 39

Energy radiated is given as:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 40

Calculate the amount of heat radiated per second by a body of surface area 12cm2 kept in thermal equilibrium in a room at temperature 20°C. The emissivity of the surface = 0.80 and H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer.

Solution 40

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 41

A solid aluminium sphere and a solid copper sphere of twice the radius are heated to the same temperature and are allowed to cool under identical surrounding temperatures. Assume that the emissivity of both the spheres is the same. Find the ratio of (a) the rate of heat loss from the aluminium sphere to the rate of heat loss from the copper sphere and (b) the rate of fall of temperature of the aluminium sphere to the rate of fall of temperature of the copper sphere. The specific heat capacity of aluminium = 900 J/kg -°C and that of copper = 390 J/kg - °C. The density of copper = 3.4 times the density of aluminium.

Solution 41

(a) Heat loss is the energy radiated

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Ratio is 1:4

(b) Emissivity is same in both cases

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Ratio is 2.9:1

Question 42

A 100 W bulb has tungsten filament of length 1.0m and radius 4×10-5m. The emissivity of the filament is 0.8 and H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer. Calculate the temperature of the filament when the bulb is operating at correct wattage.

Solution 42

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 43

A spherical ball of surface area H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer absorbs any radiation that falls on it. It is suspended in a closed box maintained at 57°C. (a) Find the amount of radiation falling on the ball per second. (b) Find the net rate of heat flow to or from the ball at an instant when its temperature is 200°C. Stefan constantH-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer.

Solution 43

(a) We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

(b) Also,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 44

A spherical tungsten piece of radius 1.0cm is suspended in an evacuated chamber maintained at 300K. The piece is maintained at 1000K by heating it electrically. Find the rate at which the electrical energy must be supplied. The emissivity of tungsten is 0.30 and the Stefan constant H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer.

Solution 44

We know

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 45

A cubical block of mass 1.0 kg and edge 5.0 cm is heated to 227°C It is kept in an evacuated chamber maintained at 27°C Assuming that the block emits radiation like a blackbody, find the rate at which the temperature of the block will decrease. Specific heat capacity of the material of the block is 400 J/kg - K.

Solution 45

Let us assume that cube is a black body

Thus,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 46

A copper sphere is suspended in an evacuated chamber maintained at 300K. The sphere is maintained at a constant temperature of 500K by heating it electrically. A total of 210W of electric power is needed to do it. When the surface of the copper sphere is completely blackened, 700W is needed to maintain the same temperature of the sphere. Calculate the emissivity of copper.

Solution 46

We know

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

In case of anybody:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

And in case of black body:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Dividing equation (1) and (2) we get

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 47

A spherical ball A of surface area 20cm2 is kept at the centre of a hollow spherical shell B of area 80cm2. The surface of A and the inner surface of B emit as blackbodies. Assume that the thermal conductivity of the material of B is very poor and that of A is very high and that the air between A and B has been pumped out. The heat capacities of A and B are 42 J/°C and 82 J/°C respectively. Initially, the temperature of A is 100H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer and that of B is 20°C. Find the rate of change of temperature of A and that of B at this instant. Explain the effects of the assumptions listed in the problem.

Solution 47

KA is high so it will conduct all heat while KB is low so it will so it will act as poor conductor.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Also H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Similarly H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 48

A cylindrical rod of length 50 cm and cross - sectional area H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer is fitted between a large ice chamber at 0°C and an evacuated chamber maintained at 27°C as shown in figure. Only small portions of the rod are inside the chambers and the rest is thermally insulated from the surrounding. The cross - section going into the evacuated chamber is blackened so that it completely absorbs any radiation falling on it. The temperature of the blackened end is 17°C when steady state is reached. Stefan constant H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer. Find the thermal conductivity of the material of the rod.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

 

Solution 48

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Also,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

From Equation (1) and (2)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Chapter 6 - Heat Transfer Exercise 102

Question 49

One end of a rod of length 20cm is inserted in a furnace at 800K. The sides of the rod are covered with an insulating material and the other end emits radiation like a blackbody. The temperature of this end is 750K in the steady state. The temperature of the surrounding air is 300K. Assuming radiation to be the only important mode of energy transfer between the surrounding and the open end of the rod, find the thermal conductivity of the rod. Stefan constant H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer.

Solution 49

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Also,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 50

A calorimeter of negligible heat capacity contains 100cc of water at 40°C. The water cools to 35°C in 5 minutes. The water is now replaced by K-oil of equal volume at 40°C Find the time taken for the temperature to become 35°C under similar conditions. Specific heat capacities of water and K-oil are 4200 J/kg - K and 2100 J/kg - K respectively. Density of K-oil = 800 kg/m3.

Solution 50

In case of water,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

In case of Kerosene,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Equating (1) and (2) we get

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 51

A body cools down from 50°C to 45°C in 5 minutes and to 40°C in another 8 minutes. Find the temperature of the surrounding.

Solution 51

I st CASE:

Average temperature is given as:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

And Average temperature that is different from surroundings is:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Now,

Rate of fall of temperature = H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

And also Rate of fall of temperature = H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer __________(1)

II nd CASE:

Average temperature is given as:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

And Average temperature that is different from surroundings is:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Now,

Rate of fall of temperature = H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

And also Rate of fall of temperature = H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 52

A calorimeter contains 50g of water at 50°C. The temperature falls to 40°C in 10 minutes. When the calorimeter contains 100g of water at 50°C, it takes 18 minutes for the temperature to become 45°CH-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer Find the water equivalent of the calorimeter.

Solution 52

We know,

Rate of heat flow is given as:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

And

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 53

A metal ball of mass 1 kg is heated by means of a 20W heater in a room at 20°C The temperature of the ball becomes steady at 50°C. (a) Find the rate of loss of heat to the surrounding when the ball is at 50°C. (b) Assuming Newton's law of cooling, calculating the rate of loss of heat to the surrounding when the ball is at 30°C (c) Assume that the temperature of the ball rises uniformly from 20°C to 30°C in 5 minutes. Find the total loss of heat to the surrounding during this period. (d) Calculate the specific heat capacity of the metal.

Solution 53

(a) We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Also,

P = H (As in steady state there is no loss of heat)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

(b) We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer (By Newton's law of cooling)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Now again,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

(c) Here net heat absorbed is:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 54

A metal block of heat capacity 80 J/°C placed in a room at 20°C is heated electrically. The heater is switched off when the temperature reaches 30°CH-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer The temperature of the block rises at the rate of 2°C/s just after the heater is switched on and falls at the rate of 0.2°C/s just after the heater is switched off. Assume Newton's law of cooling to hold. (a) Find the power of the heater. (b) Find the power radiated by the block just after the heater is switched off. (c) Find the power radiated by the block when the temperature of the block is 25°C represents the average value in the heating process, find the time for which the heater was kept on.

Solution 54

(a) Power of heater is given as:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

(b) Power Radiated is given as:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

(c) We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

And

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Question 55

A hot body placed in a surrounding of temperature θ0 obeys Newton's law of cooling  H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer. Its temperature at t = 0 is θ1. The specific heat capacity of the body is s and its mass is m. Find (a) The maximum heat that the body can lose and (b) the time starting from t = 0 in which it will lose 90% of this maximum heat.

Solution 55

(a) Maximum heat loss by body is given as:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

(b) If 90% of max. heat is lost then, temperature decrease is:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Temperature at H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Also

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

Integrating , we get

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer (From (1))

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Heat Transfer