Pex Plugs
Calculate the change in entropy of the gas?
2.0 moles of an ideal gas with Cv = 3R/2, initially confined to a container of volume 5 L and at a temperature 24 C, expand (or are compressed) against a constant external pressure of 0.8 atm until the final pressure of the gas is equal to the external pressure. During this process the system does 4,894 J of work on the surroundings. Calculate the change in entropy, Delta S, of the gas (in J / K).
Calculated V(final) using w=-pex(V2-V1) V2 = 55.342 L
Calculated T(final) using PV = nRT T2 = 269.92 K
Plugged them in Delta S = n*R*ln(V2/V1) + n*Cv,m*ln(T2/T1)
Got an answer of 39.69 but the correct answer is 44.5.
Can anyone figure out my mistake?
It perhaps unit conversion problem.
n = 2 mol
Cv = 3/2 R
V1 = 5 L
T1 = 24 deg. C = 297 K
W = 4,894 J
P = 0.8 atm = 81,060 Pa =
W = P(V2-V1)
V2 = V1 +W/P = 5 + 4894000/81060
V2 = 65.375 L = 65.375*10^-3 m^3
P2V2 = nRT2
T2 = P2V2/nR = 81,060*65.375*10^-3 / 2*8.314
T2 = 318.697 K
Tds = du + pdv
ds = (Cv/T)dT + (R/v)dv
ΔS = n* [ (3/2R ln(T2/T1) + Rln(V2/V1) ]
ΔS = 2*8.314* [1.5*ln(318.697/297 + ln(65.375/5)]
ΔS = 2*8.315*(0.10576+2.57)
ΔS = 44.49 J/K
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