Thermal Physics - Isothermal

A mole of ideal gas initially at temperature T₀ and volume V₀ undergoes a reversible isothermal expansion to volume V₁. If the ratio of specific heats is c_p/c_v = γ and if R is the gas constant, the work done by the gas is

A. Zero
B. RT₀ (V₁/V₀ )^γ
C. RT₀ (V₁/V₀ − 1)
D. c_v T₀ [1 − (V₁/V₀ )^(γ−1)]
E. RT₀ ln (V₁/V₀ )

(GR9277 #62)

Solution:

W = ∫ P dV

Ideal Gas: PV = nRT  → P = nRT / V

W = _V0∫^V₁ nRT (1/V) dV

1 mole → n = 1
Isothermal, constant T = T₀

→ W = RT_0 V0∫^V₁ (1/V) dV = RT₀ ln (V₁/V₀ )

Answer: E