Question

Assume there's 1 mol ideal mono-atomic gas in a 22.4L container at 300K. The initial entropy of the system is 100J/K. For the following processes, calculate:

a) q and w for a reversible expansion to twice the volume, isothermally.

b) $\Delta$ S and $\Delta$ G for irreversible isothermal expansion against a constant 0.5 bar external pressure, to a final internal pressure of 0.5 bar.

c) $\Delta$ U and $\Delta$ H for adiabatic reversible expansion to twice the volume.

Answer 1

a) For an isothermal expansion,

w = -nRTln(V2/V1)

So,

w = -1 x 8.314 x 300 ln(2) = -1.73 kJ

q = -w = 1.73 kJ

b) dS = 0

dG = q = 1.73 kJ

c) for adiabatic system, q = 0

dU = nCvdT

T1 = 300 K

T2 = T1(V1/V2)^y-1/y, with y = 5/3 for monoatomic gas

     = 300(0.5)^0.4 = 228 K

dU = 1 x 1.5 x 8.314 x (228-300) = -0.90 J

dH = nCpdT = 1 x 2.5 x 8.314 x (228-300) = -1.50 J