(a)
The change in entropy of the universe for each cycle.
(a)
Answer to Problem 77PQ
The change in entropy of the universe for each cycle is
Explanation of Solution
Write the expression to calculate the change in entropy of the hot reservoir.
Here,
Write the expression to calculate the change in entropy of the hot reservoir.
Here,
Write the expression to calculate the heat added to the cold reservoir.
Here, W is the work done by the engine.
Substitute the above equation in (II) to rewrite.
Write the expression to calculate the entropy change in universe.
Here,
Substitute the equation (I) and (III) in the above equation to rewrite.
Conclusion:
Substitute
Therefore, the change in entropy of the universe for each cycle is
(b)
The required more work has to be done by the Carnot engine.
(b)
Answer to Problem 77PQ
The required more work has to be done by the Carnot engine is
Explanation of Solution
Write the expression to calculate the work done by the Carnot engine.
Here,
Write the expression to calculate the efficiency of the engine.
Rewrite the equation for W using the above expression.
Write the expression to calculate the more work required.
Here,
Conclusion:
Substitute
Substitute
Therefore, the required more work has to be done by the Carnot engine is
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Chapter 22 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- (a) What is the hot reservoir temperature of a Carnot engine that has an eficiency of 42.0% and a cold reservoir temperature of 210C ? (b) What must the hot reservoir temperature be for a real heat engine that achieves 0.700 of the maximum eficiency, but still has an efficiency of 42.0% (and a cold reservoir at 27.0C )? (c) Does your answer imply practical limits to the efficiency of car gasoline engines?arrow_forward(a) What is the change in entropy if you start with 100 coins in the 45 heads and 55 tails macrostate, toss them, and get 51 heads and 49 tails? (b) What if you get 75 heads and 25 tails? (c) How much more likely is 51 heads and 49 tails than 75 heads and 25 tails? (d) Dues either outcome violate the second law of thermodynamics?arrow_forwardA system consisting of n moles of an ideal gas with molar specific heat at constant pressure Cr undergoes two reversible processes. It starts with pressure Pi and volume Vi, expands isothermally, and then contracts adiabatically to reach a final state with pressure Pi and volume 3Vi. (a) Find its change in entropy in the isothermal process. (The entropy does not change in the adiabatic process.) (b) What If? Explain why the answer to part (a) must be the same as the answer to Problem 46. (You do not need to solve Problem 46 to answer this question.)arrow_forward
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