One mole of a monatomic ideal gas at $300 K$ expands reversibly and adiabatically to twice its initial volume. Take $R = 8.314 J mo l^{- 1} K^{- 1}$ and $γ = 5/3$ . Find the work done by the gas in joules (nearest integer).

Numerical answer type, answer in J, tolerance 1.

Answer: 1384 J

For a reversible adiabatic process

T V^{γ - 1}

is constant:

T_{2} = 300 \times (1/2)^{2/3} = 189.0 K

. Then

∣ w ∣ = - Δ U = n C_{V} (T_{1} - T_{2}) = 1.5 \times 8.314 \times (111.0) = 1384 J

done by the gas.