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: CP > CV.
Defining statement: dQ = nCP 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:
CP = |
| 5
|  |
| 2
|
|
R = CV + R |
(diatomic:
|
CP |
= |
| 7
|  |
| 2
|
|
R) |
The specific heat ratio γ ≡ CP / CV
| For a monatomic
ideal gas: γ |
= |
| CP
| |
| CV
|
|
= |
| 5R
| |
| 2
|
|
* |
| 2
| |
| 3R
|
|
= |
| 5
| |
| 3
|
|