# Thermal physics

### Unit of Heat

Heat energy flows from one body to another body due to their temperature difference. It is measured in units of calorie. A calorie is the amount of heat required to raise the temperature of 1 gm of water through 1°C.

1 KiloCalorie = 103 Calories

1 Calorie = 4.186 Joule

If the temperature of a body of a mass m is raised through a temperature ΔT, then the heat, ΔQ, given to the body is

ΔQ= m.S.ΔT

where S is the specific heat of the body which is defined as the amount of heat required to raise the temperature of a unit mass of the body through 1°C. Its unit is cal/gm °C or J/Kg.K. Thermal capacity of a body is the quantity of heat required to raise its temperature through 1°C and is equal to the product of mass and specific heat of the body.

### Principle of Calorimetry

When two bodies at different temperatures are mixed, the heat will pass from a body at a higher temperature to a body at a lower temperature until the temperature of the mixture becomes constant. The principle of calorimetry implies that heat lost by a body at a higher temperature is equal to the heat gained by a body at a lower temperature assuming that there is no loss of heat to the surroundings.

### Latent Heat :

It is the amount of heat absorbed or given out by a body during the change of state when its temperature remains constant.

### Latent heat of Fusion :

It is the quantity of heat required to change unit mass of any solid substance into its liquid state at a constant temperature of fusion at its melting point. The latent heat of fusion of ice is 80 calories per gm.

### Latent heat of Vaporisation :

It is the quantity of heat required to convert unit mass of a liquid to the gaseous state at its constant temperature of vaporisation. The latent heat of vaporisation of water is 540 calories/gm at 100°C under normal atmospheric pressure when 1 gram of water gets converted into steam.temperature of vaporisation.

### Specific Heat of Gases :

In the case of solids and liquids, the change of volume, pressure or external work done during the change of temperature is negligible. There is only one value of specific heat for solids or liquids. However, when the temperature of gases is changed, there is a large change in the volume or pressure of the gases. The heat supplied will thus depend upon the condition under which the temperature changes. It implies that the specific heat has to be specified separately under the following conditions of constant volume or constnat pressure :–

1. Specific heat at constant Volume, cv :  It is the amount of heat required to raise the temperature of one gram of a gas through 1°C when the volume of the gas is constant.
• ΔQ = mcv ΔT
2. Specific heat at constant Pressure, cp :  It is the amount of heat required to raise the temperature of one gram of a gas through 10C when the pressure of the gas is kept constant.
• ΔQ = mcp ΔT

### Molar Heat Capacity :

The amount of heat required to increase the temperature of 1 mole of a gas through 1°C is called molar heat capacity. The number of moles, n, in mass m of the gas is given by n = mass of gas/molecular weight.

### Molar Specific Heat at Constant Volume, Cv:

If ΔQ is the heat required to raise the temperature of mass m gm or n moles of gas of molecular weight M at constant volume through temperature ΔT,

(ΔQ)v = mcv ΔT = nMcv  ΔT = nCv ΔT

where Cv is molar specific heat at constant volume and is equal to McV.

### Molar Specific Heat at Constant Pressure, Cp :

If ΔQ is the heat required to raise the temperature of mass m gram or n moles of gas of molecular weight M at constant pressure through temperature ΔT,

(ΔQ)p = mcp ΔT = nMcp  ΔT = nCp ΔT

where Cp is molar specific heat at constant pressure and is equal to Mcp.

For monoatomic gases, Cp = 5R/2 , Cv = 3R/2  γ = Cp/Cv=  5/3  = 1.67