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 = DU + W = (3/2)nRDT + nRDT = (5/2)nRDT
Therefore DT = (2/5)Q/nR = 1000/20 = 50 K.
T2 = T1 + DT = 100 + 50 = 150 K
(c) How much work was done by the gas during the expansion?
W = nRDT = 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)/20x103 = 150 x 10-3 m3