Sample Problem
A container of monatomic ideal gas contains just the right number of moles so that nR = 20 J/K. The gas is in state 1 such that:
P1 = 20 kPa
V1 = 100 x 10-3 m3
(a) What is the temperature T1 of the gas?
Use the ideal gas law:
PV = nRT, so:
| T1 |
= |
| P1V1
|  |
| nR
|
|
= |
| 2000
| |
| 20
|
|
= 100 K |
(b) If Q = 2500 J of heat is added to the gas, and the gas expands at constant pressure, the gas will reach a new equilibrium state 2. What is the final temperature T2?
We've already seen that, at constant pressure for a monatomic ideal gas:
| Q |
= ΔEint + W = |
| 3
| |
| 2
|
|
nRΔT + nRΔT = |
| 5
| |
| 2
|
|
nRΔT |
| Therefore ΔT |
= |
| 2 Q
| |
| 5nR
|
|
= |
| 1000
| |
| 20
|
|
= 50 K |
T2 = T1 + ΔT = 100 + 50 = 150 K
(c) How much work was done by the gas during the expansion?
W = nRΔT = 20 * 50 = 1000 J
That equation is true only for a constant pressure process.
(d) What is the final volume V2?
One approach is to bring in the ideal gas law again:
| V2 |
= |
| nRT2
| |
| P2
|
|
= |
| 20 * 150
| |
| 20 x 103
|
|
= 150 x 10-3 m3 |