One mole of a monatomic ideal gas at $300 K$ and $1 atm$ is compressed adiabatically by a constant external pressure of $4 atm$ until the gas pressure is $4 atm$ . With $R = 8.314 J mo l^{- 1} K^{- 1}$ , the entropy change of the gas is

Answer: C

Energy balance:

1.5 R (T_{2} - 300) = - 4 (V_{2} - V_{1}) \to 1.5 (T_{2} - 300) = - T_{2} + 4 (300)

in units of

R

, so

T_{2} = 1650/2.5 = 660 K

Δ S = C_{P} ln (T_{2} / T_{1}) - R ln (P_{2} / P_{1}) = 2.5 R ln 2.2 - R ln 4 = 4.862 J K^{- 1}

. It is positive (irreversible adiabatic) and not zero.