H C VERMA Solutions for Class 12-science Physics Chapter 1 - Heat and Temperature
Chapter 1 - Heat and Temperature Exercise 12
The steam point and the ice point of a mercury thermometer are marked as 80° and 20°. What will be the temperature in centigrade mercury scale when this thermometer reads 32°?
For any scale
A constant volume thermometer registers a pressure of 1.500× Pa at the triple point of water and a pressure of 2.050× Pa at the normal boiling point. What is the temperature at the normal boiling point?
A gas thermometer measure the temperature from the variation of pressure of a sample of gas. If the pressured measured at the melting point of lead is 2.20 times the pressure measured at the triple point of water, find the melting point of lead?
Pressure measured at melting point=2.2×pressure at triple point
The pressure measured by a constant volume gas thermometer is 40kPa at the triple point of water. What will be the pressure measured at the boiling point of water (100°C)?
=40× Pa; T=273+100=373 K
The pressure of the gas in a constant volume gas thermometer is 70 kPa at the ice point. Find the pressure at the steam point.
The pressure of the gas in a constant volume gas thermometer are 80 cm, 90 cm and 100 cm of mercury at the ice point, the steam point and in a heated wax bath respectively. Find the temperature of the wax bath.
In a Callender's compensated constant air pressure thermometer, the volume of the bulb is 1800 cc. When the bulb is kept immersed in a vessel, 200 cc of mercury has to be poured out. Calculate the temperature of the vessel.
A platinum resistance thermometer reads when its resistance is 80Ω and when its resistance is 90Ω. Find the temperature at the platinum scale at which the resistance is 86Ω.
Chapter 1 - Heat and Temperature Exercise 13
A resistance thermometer reads R=20.0 Ω, 27.5 Ω and 50.0Ω at the ice point (), the steam point () and the zinc point () respectively. Assuming that the resistance varies with the temperature as , find the values of , and . Here represents the temperature on Celsius scale.
Variation of resistance with temperature
Solving (i) and (ii)
A concrete slab has a length of 10 m on a winter night when the temperature is C. Find the length of the slab on a summer day when the temperature is C. The co-efficient of linear expansion of concrete is 1.0×.
A meter scale made of steel is calibrated at C to give correct reading. Find the distance between 50 cm mark and 51 cm mark if the scale is used at C. Co-efficient of linear expansion of steel is 1.1×/.
A railway track (made of iron) is laid in winter when the average temperature is C. The track consists of sections of 12.0 m placed one after the other. How much gap should be left between two much sections so that there is no compression during summer when the maximum temperature goes to C? Co-efficient of linear expansion of iron=11.
A circular hole of diameter 2.00 cm is made in an aluminium, plate at C. What will be the diameter at C? α for aluminium=2.3.
Two metre scales, one of steel and the other of aluminium, agree at C. Calculate the ratio aluminium-centimetre/steel-centimeter at (a)C, (b) C and (c) C. α for steel=1.1 and for aluminium =2.3.
A meter scale is made up of steel and measures correct length at. What will be the percentage error if this scale is used (a) on a summer day when the temperature is and (b) on a winter day when the temperature is? Coefficient of linear expansion of steel=11.
(a) In Summer
(b) In winter
A metal scale made of steel reads accurately at C. In a sensitive experiment, distances accurate up to 0.055 mm in 1 m are required. Find the range of temperature in which the experiment can be performed with this meter scale. Coefficient of linear expansion=11.
Range of temperature is from 15 to 25.
The density of water at 0 is 0.998 g/ and at 4 is 1.00 g/. Calculate the average coefficient of volume expansion of water in the temperature range 0 to 4.
Find the ratio of lengths of an iron rod and an aluminium rod for which the difference in the lengths is independent of temperature. Coefficients of linear expansion of iron and aluminium are and respectively.
A pendulum clock gives correct time at 20 at a place where, g=9.800 m/. The pendulum consists of a light steel rod connected to a heavy ball. It is taken to a different place where g=9.788 m/. At what temperature will it give correct time? Coefficient of linear expansion of steel=12.
Since, time period remains same
An aluminium plate fixed in a horizontal position has a hole diameter 2.000 cm. A steel sphere of diameter 2.005 cm rests on this hole. All the lengths refer to a temperature of 10. The temperature of the entire system is slowly increased. At what temperature will the fall down? Coefficient of linear expansion of aluminium is 23 and that of steel is 11.
Ball will fall down when diameter of both plate and sphere becomes equal.
at T= at T
A glass window is to be fit in an aluminium frame. The temperature on the working day is 40 and the glass window measures exactly 20 cm× 30 cm. What should be the size of the aluminium frame so that there is no stress on the glass in winter even if the temperature drops to 0 ? Coefficients of linear expansion for glass and aluminium are 9.0 and 24 respectively.
For no stress in winter final length and breadth of glass and aluminium frame must be the same.
The volume of a glass vessel is 1000 cc at 20. What volume v of mercury should be poured into it at this temperature so that the volume of the remining space does not change with temperature? Coefficients of cubical expansion of mercury and glass are 1.8 and 9.0 respectively.
Since, volume of air (space) remains same.
So, change in volume of Hg=change of volume of glass
An aluminium can of cylindrical shape contains 500 of water. The area of inner cross-section of the can is 125. All measurements refer to 10. Find the rise in the water level if the temperature increases to 80. The coefficient of linear expansion of aluminium=23 and the average coefficient of volume expansion of water=3.2 respectively.
Change in volume of water
Base expansion of can is neglected
So, increase in height of water=cm
A glass vessel measures exactly 10 cm×10 cm ×10 cm at 0. It is completely filled with the mercury at this temperature. When the temperature is raised to 10, 1.6 of mercury overflows. Calculate the coefficient of volume expansion of mercury. Coefficient of linear expansion of glass=6.5.
The densities of wood and benzene at 0 are 880 kg/ and 900 kg/ respectively. The coefficients of volume expansion are 1.2 for wood and 1.5 for benzene. At what temperature will a piece of wood just sink in benzene?
When wood just sinks in benzene
Weight of wood=Buoyancy force
A steel rod of length 1 m rests on a smooth horizontal base. If it is heated from 0 to 100, what is the longitudinal strain developed?
Since, there is no opposition in expansion of length, no stress develops and hence no longitudinal strain developed.
A steel rod is clamped at its two ends and rests on fixed horizontal base. The rod is unstrained at 20. Find the longitudinal strain developed in the rod if the temperature rises to 50. Coefficient of linear expansion of steel=1.2.
A steel wire of cross-sectional area 0.5 is held between two fixed supports. If the wire is just taut at 20, determine the tension when the temperature falls to 0. Coefficient of linear expansion of steel is 1.2 and its Young'smodulus is 2.0.
A steel rod is rigidly clamped at two ends. The rod is under zero tension at 20. If the temperature rises to 100, what force will the rod exert on one of the clamps. Area of cross-section of the rod=2.00 . Coefficient of linear expansion of steel=12.0 and Young's modulus of steel=2.00.
Chapter 1 - Heat and Temperature Exercise 14
Two steel rods and an aluminium rod of equal length and equal cross-section are joined rigidly at their ends as shown in figure below. All the rods are in the state of zero tension at 0. Find the length of the system when the temperature is raised to θ. Coefficient of linear expansion of aluminium and steel are and respectively. Young's modulus of aluminium is and of steel is .
Let final length of the system be l
A steel ball initially at a pressure of 1.0Pa is heated from 20 to 120 keeping its volume constant. Find the inside the ball. Coefficient of linear expansion of steel=12 and bulk modulus of steel=1.6.
Show that moment of inertia of a solid body of any shape changes with temperature as , where is the moment of inertia at 0 and α is the coefficient of linear expansion of the solid.
Moment of inertia=Mass
[By binomial expansion]
A torsional pendulum consists of a solid disc connected to a thin wire () at its center. Find the percentage change in the time period between peak winter (5) and peak summer (45).
Time period of torsional pendulum
% change =
A circular disc made of iron is rotated about its axis at a constant velocity . Calculate the percentage change in the linear speed of the particle of the rim as the disc is slowly heated from 20 to 50 keeping the angular velocity constant. Coefficient of linear expansion of iron=.
% change in linear speed=
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