An airtight freezer holds n moles of air at 28.0 degree C and 1.00 atm. The air

Question

An airtight freezer holds n moles of air at 28.0 degree C and 1.00 atm. The air is then cooled to -19.5 degree C. (a)What is the change in entropy of the air if the volume is held constant? x nR (b)What would the entropy change be if the pressure were maintained at 1.00 atm during the cooling? airtight freezer holds n moles of air at 28.0 degree C and 1.00 atm. The air is then cooled to -19.5 degree C. (a)What is the change in entropy of the air if the volume is held constant? x nR (b)What would the entropy change be if the pressure were maintained at 1.00 atm during the cooling? x nR

Explanation / Answer

T1 = 28 deg C = 301 K ; P = 1 atm ; T2 = -19.5 deg C = 254 K

a)Volume is constant.

dQ = dU + P dV

dQ = dU = n Cv dT

for ditomic gases, Cv = 5R/2

change in entropy = n Cv ln(T1/T2)

dS = n 5/2 R ln [(301/254)] = 0.424 nR

Hence, dS = 0.424 nR

b)dQ = n Cv dT + P dV = 5 n R/2 dt + n R dt = 7 n R/2 dT

dS = 7nR/2 ln(T2/T1)

dS = 7 n R/ 2 ln (301/254)] = 0.59 nR

Hence, dS = 0.59 nR

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