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Question

Explain heat capacity.


Solution

When a gas is heated at constant volume i.e. gas uses all the heat which is given to it for increasing its internal energy. Hence if the temperature of one mole of a gas is raised through 1 degree C, the molar heat capacity is given itself at constant volume by an increase in internal energy.
But when a gas is heated to constant pressure there will be an expansion of gas i.e. increase in volume take place and some external work will b done. For this, some extra heat is required which should be given to the gas to perform the external work.
Hence the molar heat capacity of a gas at constant pressure must be greater than molar heat capacity of a gas at constant volume.
CP > CV
When gas is heated through 1 degree C at constant pressure, the difference between these will give the work done by one mole of the gas in the expansion.
As we know that at constant pressure work done by the gas in expansion is given mathematically as:
w=PΔV
For one mole of an ideal gas:
PV = RT .... (1)
When temperature is raised by 1C from T to T + 1 so that volume becomes V+ΔV, then
P(V+ΔV)=R(T+1)  ..... (2)
Subtracting equation (1) from equation (2), we get:
PΔV=R
Thus, At constant pressure work done by one mole of the an ideal gas in expansion when heated through 1C is equal to R. hence,
CP – CV = R
Thus, the difference between molar heat capacity of a gas at constant pressure, CP and at constant volume, CV is equal to the gas constant R. i.e. 1.987 cal or 8.314 J

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