A cylinder with a piston contains 0.250mol of oxygen at 2.40×105Pa and 355K. The

Question

A cylinder with a piston contains 0.250mol of oxygen at 2.40×105Pa and 355K. The oxygen may be treated as an ideal gas. The gas first expands isobarically to twice its original volume. It is then compressed isothermally back to its original volume, and finally it is cooled isochorically to its original pressure.

Part A

Compute the temperature during the isothermal compression.

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Part B

Compute the maximum pressure.

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Part C

Compute the total work done by the piston on the gas during the series of processes.

Explanation / Answer

P1 = 2.4*10^5 Pa

T1 = 355 K

n = 0.25 m

V1 = n*R*T/P1 = 0.25*8.314*355/(2.4*10^5) = 3.1*10^-3 m^3

after isobaric expansion

P2 = P1

V2 = 2V1

T2 = 2T1

after isothermal compression

T3 = T2 = 2*T1

V3 = V1

P3*V3 = P2*T2

P3*V1 = P1*2*T1

P3 = 2*P1

after isochoric process

V4 = V3 = V1

P4 = P1

T4 = 2*T1

part A

T3 = 2*T1 = 710 K

part B

Pmax = 2*P1 = 4.8*10^5 Pa

part(c)

Wisobaric = P1*(V2-V1) = P1*(2V1-V1) = P1*V1 = +737.8 J

Wisothermal = n*R*T*log(V3/v2) = 0.5*8.314*2*355*log(1/2) = -888.5 J

W isochoric = 0

Wtotal = -150.7 J

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