20.0 dm3 of an ideal gas 'X' at 600 K and 0.5 MPa undergoes isothermal reversible expansion until pressure of the gas is 0.2 MPa. Which of the following option is correct? (Given: 2 = 0.3010 and 5 = 0.6989)
- w = -9.1 kJ, U = 0, H = 0, q = 9.1 kJ
- w = 9.1 J, U = 9.1 J, H = 0; q = 0
- w = -3.9 kJ, U = 0, H = 0; q = 3.9 kJ
- w = +4.1 kJ, U = 0, H = 0; q = -4.1 kJ
Answer
(1) w = -9.1 kJ, U = 0, H = 0, q = 9.1 kJ
Solution
For an ideal gas at constant temperature, U = 0 and H = 0.
Work in isothermal reversible expansion:
w = -2.303 nRT P1P2, and nRT = P1V1
P1V1 = (0.5 106 Pa)(20.0 10-3 m3) = 1.0 104 J
0.50.2 = 2.5 = 5 - 2 = 0.6989 - 0.3010 = 0.3979
w = -2.303 1.0 104 0.3979 J
w = -9.16 103 J -9.1 kJ
First law: U = q + w = 0
q = -w = +9.1 kJ
Answer: (1)