Question

An amount of nitrogen gas is used as the system of a heat engine. There are four processes in the cycle. 1. Starting at 20 atm and 2 liters, the gas expands isothermally to 10 liters and 800K. 2. The gas then cools isochorically to 400K. 3. Then the gas is compressed isothermally to 2 liters again. 4. Finally, the gas is heated isochorically again to 800K and its starting point. What is the amount of work delivered per cycle?

Answer 1

Work done during isothermal expansion, W1= nRT1 ln (v1/v2)

n= number of moles R- gas constant

W1= nR*800* ln (2/10) = nR* 800* -1.609 = -1287.55 nR

This work is done by the system.

Work done during isothermal compression,W2= nRT2 ln (v2/v1) = nR*400* ln(10/2) = nR* 400*1.609 = 643.77 nR

This work is done on the system.

No work is done during isochoric process.

So net work done per cycle W= w1+w2 = -1287.55nR + 643.77 nR = -643.78 nR

R= 8.314 J K-1 mol-1

W= -643.78*8.314*n = -5352.38n

n- number of moles of nitrogen

-ve sign shows net work is by the system.