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# Thermodynamics

## Thermodynamics PDF Notes, Important Questions and Formulas

Thermodynamics

HEAT

The energy that is being transferred between two bodies or between adjacent parts of a body as a result of temperature difference is called heat. Thus, heat is a form of energy. It is energy in transit whenever temperature differences exist. Once it is transferred, it becomes the internal energy of receiving body. If should be clearly understood that the word “heat” is meaningful only as long as the energy is being transferred. Thus, expressions like “heat in a body” or “heat of body” are meaningless.

When we say that a body is heated it means that its molecules begin to move with greater kinetic energy.

S.I. unit of heat energy is joule (J). Another common unit of heat energy is calorie (cal).

Mechanical Equivalent of Heat

In early days heat was not recognised as a form of energy. Heat was supposed to be something needed to raise the temperature of a body or to change its phase. Calorie was defined as the unit of heat. A number of experiments were performed to show that the temperature may also be increased by doing mechanical work on the system. These experiments established that heat is equivalent to mechanical energy and measured how much mechanical energy is equivalent to a calorie.

Specific Heat

Specific heat of substances is equal to heat gain or released by that substance to raise or fall its temperature by 1℃ for a unit mass of substance.

When a body is heated, it gains heat. On the other hand, heat is lost when the body is cooled. The gain or loss of heat is directly proportional to:

1. the mass of the body △Q ∝ m
2. rise or fall of temperature of the body △Q ∝ △T

△Q ∝ m △T or   Q α m s T

Or dQ ∝ m s d T    or   Q=m ʃ sdT

Where S is a constant and is known as the specific

heat of the body s= S.I. unit of s is joule/kg-kelvin

and C.G.S unit is cal/gm℃

Specific heat of water: s=4200j/kg℃=1000cal/kg℃=1 Kcal/kg℃=1 cal/gm℃

Specific heat of steam= half of specific heat of water= specific heat of ice

Heat capacity or thermal capacity:
Heat capacity of a body is defined as the amount of heat required to rasie the temperature of that body by 1℃. If ‘m’ is the mass and‘s’ the specific heat of the body, then

Heat capacity=m s.

Units of heat capacity in: CGS system is,

Cal ℃-1; SI unit is, JK-1

Relation between specific heat and
Water equivalent:

It is the amount of water which requires the same amount of heat for the same temperature rise as that of the object

CONCEPT OF AN IDEAL GAS
A gas has no shape and size and can be contained in a vessel of any size or shape. It expands indefinitely and uniformly to fill the available space. It exerts pressure on its surroundings. The gases whose molecules are point masses (mass without volume) and do not attract each other are called ideal or perfect gases. It is a hypothetical concept which can't exist in reality. The gases such as hydrogen, oxygen or helium which cannot be liquified easily are called permanent gases. An actual gas behaves as ideal gas most closely at low pressure and high temperature.

Ideal gas Equation

According to this equation.

In this equation n=number of moles of the gas=

m=total mass of the gas

M= molecular mass of the gas

R= Universal gas constant

=8.31 J/mol-K

=2.0 cal/mol-K

KINETIC THEORY OF GASES

Kinetic Theory of gases is based on the following basic assumptions.

1. A gas consists of very large number of molecules. These molecules are identical, perfectly elastic and hard spheres. They are so small that the volume of molecules is negligible as compared with the volume of the gas.
2. Molecules do not have any preferred direction of motion, motion is completely random.
3. These molecules travel in straight lines and in free motion most of the time. The time of the collision     between any two molecules is very small.
4. The collision between molecules and the wall of the container is perfectly elastic. It means kinetic energy is conserved in each collision.
5. The path travelled by a molecule between two collisions is called free path and the mean of this distance travelled by a molecule is called mean free path.
6. The motion of molecules is governed by Newton’s law of motion
7. The effect of gravity on the motion of molecules is negligible.

EXPRESSION FOR THE PRESSURE OF A GAS:

Let us suppose that a gas is enclosed in a cubical box having length? Let there are ‘N’ identical molecules, each having mass ‘m’ Since the molecules are of same mass and perfectly elastic, so their mutual collisions result in the interchange of velocities only. Only collisions with the walls of the container

Contribute to the pressure by the gas molecules. Let us focus on a molecule having velocity v1 and components of velocity  along x, y, and z-axis as shown in figure.

Co-ordinate of the gases

(P, V, T) is the coordinate of the gas

If initial condition of gas is given by (P1, V1, T1) and final condition of gas is given by (P2,V T) such as

Then (P, V, T) define situation of gas. When a gas changes from one coordinate system to another co-ordinate system, then we have to follow a process.