Consider 2.00 mol of an ideal gas with a constant-volume molar specific beat of 12.5 1/(mol-K), an initial

Question

Consider 2.00 mol of an ideal gas with a constant-volume molar specific beat of 12.5 1/(mol-K), an initial temperature of 22 8 °C, and an initial pressure of 5 610 x 10 Pa. The state of the gas is changed to a final temperature of 43.6 °C and a final pressure of 3.270 x 10 Pa

The gas constant is 8.31 j/(mol-K).

What is the change in the entropy Delta S of the gas during this process

J/K

Answer 1

From dU = TdS - PdV, you know dS = dU/T - (P/T) dV

You know dU = nC_vdT P/T = nR/V

ΔS = Int (nC_V/T)dT - Int(nR/V)dV = nC_vln(T₂/T₁) - nRln(V₂/V₁)

You can plug into this. Make sure that T's are in Kelvin and R = 8.314 J/mole-K

V₂/V₁ = T₂/T₁ * P₁/P₂ (any units are ok as long as physical quantities for two states are in the same units.

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