Constant Pressure
A constant pressure process is called an isobaric process. An example is a gas in a container sealed with a piston that is free to slide up and down.
If heat is added the temperature goes up and the system expands, so work is done.
The full First Law applies:
DU = Q - W
The P-V diagram for this process is a horizontal line, so the work done is simply:
W = P DV = nR DT
For a monatomic ideal gas:
| DU |
= |
| 3
|  |
| 2
|
|
nR DT |
Plugging this into the First Law gives:
Q = DU + W
| Q |
= |
| 3
| |
| 2
|
|
nR DT |
+ |
nR DT |
= |
| 5
| |
| 2
|
|
nR DT |
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 DT
For an ideal gas, applying the First Law of Thermodynamics told us that for a monatomic ideal gas:
| Q |
= DU + W =
|
| 3
| |
| 2
|
|
nR DT |
+ nR DT |
= |
| 5
| |
| 2
|
|
nR DT |
| So, for a monatomic ideal gas: CP |
= |
| 5
| |
| 2
|
|
R |
In general CP = CV + R, so 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 g. For a monatomic ideal gas we have:
| g |
= |
| CP
| |
| CV
|
|
= |
| 5R
| |
| 2
|
|
* |
| 2
| |
| 3R
|
|
= |
| 5
| |
| 3
|
|