Two moles of a monatomic ideal gas at $300 K$ and $10 L$ expand reversibly to $20 L$ , once isothermally and once adiabatically. Use $R = 8.314 J mo l^{- 1} K^{- 1}$ . Select the correct statement(s).

AThe work done by the gas in the isothermal expansion is about $3.46 kJ$ .
BThe final temperature in the adiabatic expansion is about $238 K$ .
CThe work done by the gas in the adiabatic expansion is about $2.77 kJ$ .
DThe final pressure is higher for the adiabatic expansion than for the isothermal one.

Answer: A, C

Isothermal:

w = n RT ln 2 = 2 \times 8.314 \times 300 \times 0.693 = 3.46 kJ

(statement 1 true). Adiabatic:

T_{2} = 300 \times 2^{- 2/3} = 189 K

, not

238 K

(that uses the exponent

1/3

), so statement 2 is false. Then

w = n C_{V} (T_{1} - T_{2}) = 3 \times 8.314 \times (111) \approx 2.77 kJ

(statement 3 true). At the same final volume the adiabatic gas is colder, so its pressure is lower, and statement 4 is false.