A heat engine is run between two reservoirs at temperatures TH and Tc. One cycle of this engine involves an ideal gas going through two isothermal processes and two adiabatic processes, as shown in the p-V diagram below. All four of these processes are reversible.

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Chapter1: Units, Trigonometry. And Vectors
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a. What is the name given to this cycle, and why is it important?

The volume of the ideal gas at point 1 is V1, etc. By analysing the adiabatic processes, we find that:

V_2/V_1 = V_4/V_3

b. The work done during the isothermal processes is WC (between points 1 and 2) and WH (between points 3 and 4). Find an expression for the fraction WC / WH in terms of TC and TH.

c. Apply the First Law of Thermodynamics to the isothermal processes to show that the efficiency of this cycle is (please see the image with the corresponding formula for question c)

d. Use the Second Law of Thermodynamics to explain why no heat engine can be more efficient than a perfectly reversible engine. You may wish to include a heat flow diagram in your answer.

A heat engine is run between two reservoirs at temperatures TH and Tc. One cycle of this engine involves an ideal
gas going through two isothermal processes and two adiabatic processes, as shown in the p-V diagram below. All
four of these processes are reversible.
Р
3
Isotherms
Он
2
Adiabats
4
Qc
1
TH
Tc
V
Transcribed Image Text:A heat engine is run between two reservoirs at temperatures TH and Tc. One cycle of this engine involves an ideal gas going through two isothermal processes and two adiabatic processes, as shown in the p-V diagram below. All four of these processes are reversible. Р 3 Isotherms Он 2 Adiabats 4 Qc 1 TH Tc V
c. Apply the First Law of Thermodynamics to the isothermal processes to show that the efficiency of this cycle
is
η=1.
Tc
TH
Transcribed Image Text:c. Apply the First Law of Thermodynamics to the isothermal processes to show that the efficiency of this cycle is η=1. Tc TH
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