Heat Capacity at Constant Pressure
For an ideal gas at constant pressure, it takes more heat to achieve the
same temperature change compared to a constant volume process.
 At constant volume, all the heat added goes into raising the temperature.
 At constant pressure, some of the heat added goes into doing work.
Conclusion: C_{P} > C_{V}.
Defining statement: dQ = nC_{P} dT
From the 1st Law of Thermodynamics: dQ =
dE  dW
At constant pressure: dW =  P dV =  nR dT.
For a monatomic ideal gas, where 
dE 
= 
3
 
2


nR dT 
, we get: 
dQ 
= 
3
 
2


nR dT 
+ nR dT 
= 
5
 
2


nR dT 
Thus for a monatomic ideal gas:
C_{P} = 
5
 
2


R = C_{V} + R 
(diatomic:

C_{P} 
= 
7
 
2


R) 
The specific heat ratio γ ≡ C_{P} / C_{V}
For a monatomic
ideal gas: γ 
= 
C_{P}
 
C_{V}


= 
5R
 
2


* 
2
 
3R


= 
5
 
3

