Specific Heat Capacities of a Gas | Physics Grade XI

Specific Heat Capacities of a Gas

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Specific Heat Capacities of a Gas | Physics Grade XI

Specific Heat Capacities of a Gas

Specific Heat capacities of a gas
When a gas is heated, its volume and pressure change to a greater extent. The gas can be heated at constant pressure as well as at constant volume the amount of heat required to raise the temperature of a gas through same value at constant pressure and at constant volume is different. So, a gas has two types of specific heat capacities: (1) At constant pressure Cp and (2) At constant volume Cv.

1. Heat capacity at constant volume: It is defined as the amount of heat required to increase the temperature of 1kg substance by 1 K at constant volume.

Molar heat of a gas at constant pressure: It is defined as the amount of heat required to raise the temperature of one-mole gas through one Kelvin at constant pressure. It is denoted by Cv and its unit is J mol-1 K-1. If Q is the amount of heat required to raise the temperature of n-mole of a gas through ΔT at constant pressure, the molar heat capacity of the gas is

Cv = Q / n ΔT
If M is the molecular mass then
Cv = Mcv

2. Heat capacity at constant pressure: It is defined as the amount of heat required to increase the temperature of 1kg substance by 1 K at constant pressure.

Molar heat of a gas at constant pressure: It is defined as the amount of heat required to raise the temperature of one-mole gas through one Kelvin at constant pressure. It is denoted by Cp and its unit is J mol-1 K-1.

If Q is the amount of heat required to raise the temperature of n-mole of a gas through ΔT at constant pressure, the molar heat capacity of the gas is

Cp = Q/ n ΔT

If M is the molecular mass then

Cp = Mcp

Important question:

Q. Why Cp is greater than Cv?
When pressure is constant, the heat required is used both in increasing the internal energy of the gas as well as in doing work against external pressure, since dQ = dU + dW. But when volume is constant, dW = P dV where P dV = 0, then no work is done, and hence the heat supplied is only used to increase the internal energy of the gas. Therefore, Cp is greater than Cv.

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