One mole of an ideal gas at 25 degree C is held in a cylinder by a piston at a p

Question

One mole of an ideal gas at 25 degree C is held in a cylinder by a piston at a pressure of 200 atm. Compare the work done by the gas during the following expansions a) The piston is released suddenly, irreversibly, and isothermally in three stages, with time for equilibration between stages: first to 100 atm, then to 50 atm, and finally to 10 atm. b) A reversible isothermal reversible expansion from 200 to 10 atm at 25 degree C. c) The gas is warmed at constant pressure to the final volume of the expansions in (a) and (b). Then the gas is cooled at constant volume back to 25 degree C.

Explanation / Answer

Work done by isothermal process is expressed by following equation

W=nRTln(Vf/Vi)

Where n= number of moles present

R= universal gas constant 8.314Jmol-1K-1

T= temerature in degree centigrade

Vf= final volume in atm

Vi= initial volume in atm

Now case#1: When piston is released to 100atm

W=nRTln(Vf/Vi)

W=1*8.314*25*ln(1/2)

W= -144.07J

Case#2 When piston is released to 50atm

W=1*8.314*25*ln(1/4)

W= -288.14J

Case#3 When piston is released to 10 atm

W=1*8.314*25*ln(1/20)

W= -622.66J

Part b: Here the piston is expanded to 10atm from 200 atm.Hence the amount of work done will be the same as case#3 excluded the negative sign.

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