Ideal Gas Entropy Changes - Colby College [PDF]

Entropy and the Ideal Gas Ideal gas: (∂U ∂V )T = 0 dU = CV dT

S

for all processes

dU = dq - P dV T or V

dq = dU + P dV dqrev dT nR dS = T = CV T + V dV at constant V dT ⌠ ∆S = CV T ⌡ T2 ∆S = CV ln T   1

assume Cv = cst

at constant T V2 ⌠nR ∆S =  V dV = nR ln V  ⌡  1 dH = dU + PdV + VdP = dqrev – PdV + PdV + VdP dqrev = dH – VdP = CP dT – VdP dT nR dS = CP dP T P at constant P T2 dT ⌠ ∆S = CP T = CP ln T  ⌡  1

assume CP = cst

T2 P  ∆S = CP ln T  - nR ln  2 P1  1

3 Example: 1 mole ideal monatomic gas: CV = 2 R = 12.5 J/K double T at cst.V, ∆S = 12.5 J/K ln 2 = 8.6 J/K double T at cst P , ∆S = 20.8 J/K ln 2 = 14.4 J/K double V at cst T , ∆S = 8.314 J/K ln 2 = 5.8 J/K

Colby College

Pext = P