Heat Capacity at Constant Pressure
For an ideal gas at constant pressure, it takes more heat to achieve the same temperature change than it does at constant volume. At constant volume all the heat added goes into raising the temperature. At constant pressure some of the heat goes to doing work.
Q = nCP ΔT
For an ideal gas, applying the First Law of Thermodynamics tells us that heat is also equal to:
Q = ΔEint + W
At constant pressure W = PΔV = nR ΔT
| For a monatomic ideal gas, where |
ΔEint |
= |
| 3
|  |
| 2
|
|
nR ΔT |
, we get: |
| Q |
= |
| 3
| |
| 2
|
|
nR ΔT |
+ nR ΔT |
= |
| 5
| |
| 2
|
|
nR ΔT |
| So, for a monatomic ideal gas: CP |
= |
| 5
| |
| 2
|
|
R |
For diatomic and polyatomic ideal gases we get:
| diatomic: CP |
= |
| 7
| |
| 2
|
|
R |
polyatomic: CP = 4R
The ratio CP / CV
It turns out that the ratio of the specific heats is an important number. The symbol we use for the ratio is γ. For a monatomic ideal gas we have:
| γ |
= |
| CP
| |
| CV
|
|
= |
| 5R
| |
| 2
|
|
* |
| 2
| |
| 3R
|
|
= |
| 5
| |
| 3
|
|