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A nonreversible heat engine operates between a

Chapter 18, Problem 89GP

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QUESTION:

Problem 89GP

A nonreversible heat engine operates between a high-temperature reservoir at Th = 810 K and a low-temperature reservoir at Tc = 320 K. During each cycle the engine absorbs 660 J of heat from the high-temperature reservoir and performs 250 I of work. (a) Calculate the total entropy change ∆Stot for one cycle. (b) How much work would a reversible heat engine perform in one cycle if it operated between the same two temperatures and absorbed the same amount of heat? (c) Show that the difference in work between the nonreversible engine and the reversible engine is equal to Tc∆Stot.

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QUESTION:

Problem 89GP

A nonreversible heat engine operates between a high-temperature reservoir at Th = 810 K and a low-temperature reservoir at Tc = 320 K. During each cycle the engine absorbs 660 J of heat from the high-temperature reservoir and performs 250 I of work. (a) Calculate the total entropy change ∆Stot for one cycle. (b) How much work would a reversible heat engine perform in one cycle if it operated between the same two temperatures and absorbed the same amount of heat? (c) Show that the difference in work between the nonreversible engine and the reversible engine is equal to Tc∆Stot.

ANSWER:

Step 1 of 4

Here, we have to calculate the efficiency of a non-reversible heat engine, the work done by a reversible heat engine. We have to prove the difference in work done between a non-reversible and reversible heat engine is, .

The equation for the increase in entropy of a system,

 -----(1)

Where,  - Entropy increases in the cold reservoir

              - Entropy decrease in the hot reservoir

The equation for the efficiency of a non-reversible heat engine is,

-------(2)

Where, - Temperature of the cold reservoir

             - Temperature of the hot reservoir

a)

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