Two moles of an ideal gas at $300 K$ and $10 atm$ expand isothermally against a constant external pressure of $1 atm$ until the pressure is $1 atm$ . The gas is then compressed back isothermally and reversibly to $10 atm$ . Taking $R = 8.314 J mo l^{- 1} K^{- 1}$ , the net heat released to the surroundings over this two-step cycle is

Answer: C

Expansion:

w_{b y} = n RT (1 - P_{2} / P_{1}) = 0.9 n RT

. Compression:

w_{o n} = n RT ln 10 = 2.303 n RT

. Net work done on the gas

= n RT (ln 10 - 0.9) = (2) (8.314) (300) (2.3026 - 0.9) /1000 = 7.00 kJ

. The gas returns to its initial state (

Δ U = 0

), so the heat released equals this net work:

7.00 kJ