3. The Stirling cycle (top) and the Ericsson cycle are similar to the Carnot cyc

Question

3. The Stirling cycle (top) and the Ericsson cycle are similar to the Carnot cycle because these cycles involve isothermal heat intake and isothermal heat rejection As shown in the diagram, the Stirling cycle is 1-2 isothermal expansion with heat transfer FROM the surroundings, 2-3 isochoric compression with heat transfer TO the surroundings, 3-4 isothermal compression with heat transfer TOthe surroundings and 4- 1 isochoric compression with heat transfer FROM the surroundings. The Ericsson cycle is similar, except that the two isochoric process are replaced by two isobaric processes.

Explanation / Answer

for the path, work done during W1-2 ( isothermal process)= -integral of PdV= -nRTH ln (Vmax/Vmin)

For the path W2-3( constant volume process) W2-3= 0

For the path 3-4 ( again isothermal process), W3-4= -nRTTC ln (Vmin/Vmax)

For the path 4-1 ( again constant volume process) W4-1=0

for isothermal proceesess, W1-2 and W4-1, change in intetnal energy and heat energy are related to work as deltaU= Q+W =0 and Q =-W

for the constant volume processes 2-3 , deltaU= CV*(T3-T2) and for 4-1, deltaU= CV*(T1-T4)

efficiency = -deltaW/delta Q = -(W1-2 +W3-4)/(Q1-2 +Q4-1) = nR* ln (Vmax/Vmin)*(TH-TC)/(nRTH*ln(Vmax/Vmin)+CV*(TH-TC)

= (TH-TC)*nRTHln (Vmax/Vmin)/{ nRTHln (Vmax/Vmin)+CV*(TH-TC)

For reversible process , efficiency = (TH-TC)*nRTH*ln(Vmax/Vmin)/nRTH*ln(Vmax/Vmin)

For reversible process,   efficiency = (TH-TC)/TC same as carnot efficiency.

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