One mole of a diatomic ideal gas ( C V,m = (5/2) R ) begins in a state with P 1

Question

One mole of a diatomic ideal gas ( CV,m = (5/2) R ) begins in a state with P1 = 2.00 bar and T1 = 400.0 K. It is expanded reversibly and adiabatically until the volume of the gas has doubled; then it is expanded irreversibly and isothermally against vacuum until the volume has doubled again, after which it is heated reversibly at constant volume to 450.0 K. Finally, the gas is compressed reversibly and isothermally until a final state with P2 = 2.00 bar and T2 = 450.0 K is reached. Calculate Delta S for the gas.

Explanation / Answer

gamma =1.4

PV^gamma = constant

so, V2= 2V1

P2 =0.379 P1 = 0.7578 bar

T2= 303.14 K

delta s1 = R lnv3/v2 = 5.7628 J/K

delta s2 = cv ln T3/T2 = 2.5*8.314*ln450/303.14 = 3.284 J/k

T3=450 K, V3= 4V1 =2V2 ,P3 = 0.5624 bar

T4 =450K,P4 = 2bar, V4= 0.5624 V1

delta s3 = R lnv4/v3 =-16.31 J/K

delta S = delta S1+delta S2+delta S3 =5.7628+3.284 -16.31 = -7.2632 J/K

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