A sample of gas at temperature T is adiabatically expanded to double its volume. Adiabatic constant for the gas is γ = 3/2. The work done by the gas in the process is: (μ = 1 mole)
Options

Question

A sample of gas at temperature T is adiabatically expanded to double its volume. Adiabatic constant for the gas is γ = 3/2. The work done by the gas in the process is: (μ = 1 mole)

G1 Physics · Accepted Answer

For adiabatic process: T V ( γ V^(γ V ( γ - 1) = constant Given: V(final) = 2V(initial) γ = 3/2 Therefore: T(final) = T/√2 Work done by the gas: W = nR[T - T(final)]/(γ - 1) For n = 1 mole: W = R[T - T/√2]/(1/2) = 2RT(1 - 1/√2) = RT(2 - √2) According to the source, Option D is the keyed answer.