A sample of 1 mole gas at temperature T is adiabatically expanded to double its volume. If adiabatic constant for the gas is γ = 3/2, then the work done by the gas in the process is:
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A sample of 1 mole gas at temperature T is adiabatically expanded to double its volume. If adiabatic constant for the gas is γ = 3/2, then the work done by the gas in the process is:

G1 Physics · Accepted Answer

For an adiabatic process: TVᵞ⁻¹ = constant Given: γ = 3/2 Vf = 2V Therefore: T V¹ᐟ² = Tf(2V)¹ᐟ² Hence: Tf = T/√2 Work done by one mole of gas: W = R(T - Tf)/(γ - 1) = R[T - T/√2]/(1/2) = 2RT(1 - 1/√2) = RT(2 - √2)