Ch 21: Heat Engines and Refrigerators

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 21: Heat Engines and Refrigerators

Problem 22

Chapter 21, Problem 22

Which, if any, of the heat engines in FIGURE EX21.22 violate (a) the first law of thermodynamics or (b) the second law of thermodynamics? Explain.

Verified step by step guidance

Step 1: Review the first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred or transformed. In the context of heat engines, this means the total energy input must equal the sum of the work output and the heat rejected.

Step 2: Examine the second law of thermodynamics, which states that no heat engine can be 100% efficient. Some energy must always be rejected as waste heat to a lower-temperature reservoir.

Step 3: Analyze the heat engines in FIGURE EX21.22. For each engine, check whether the energy input equals the sum of the work output and heat rejected. If this condition is violated, the engine violates the first law of thermodynamics.

Step 4: For each engine, calculate the efficiency using the formula:

e = \frac{W}{Q}

, where

W

is the work output and

Q

is the heat input. Compare the efficiency to the theoretical maximum efficiency given by the Carnot efficiency formula:

e = \frac{(T_{h} - T_{c})}{T_{h}}

, where

T_{h}

and

T_{c}

are the temperatures of the hot and cold reservoirs, respectively.

Step 5: Determine if any engine violates the second law of thermodynamics by achieving an efficiency greater than the Carnot efficiency or by failing to reject waste heat. Summarize your findings for both laws for each engine in the figure.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

First Law of Thermodynamics

The First Law of Thermodynamics, also known as the law of energy conservation, states that energy cannot be created or destroyed, only transformed from one form to another. In the context of heat engines, this means that the total energy input into the system must equal the total energy output, accounting for work done and heat transferred. Any violation of this principle would imply an unaccounted energy source or loss.

Second Law of Thermodynamics

The Second Law of Thermodynamics states that in any energy transfer or transformation, the total entropy of a closed system can never decrease over time. This implies that heat cannot spontaneously flow from a colder body to a hotter body without external work. In terms of heat engines, this law sets a limit on the efficiency of the engine, as some energy will always be lost as waste heat.

Heat Engine Efficiency

Heat engine efficiency is a measure of how well a heat engine converts heat energy into work. It is defined as the ratio of the work output to the heat input, often expressed as a percentage. The efficiency of a heat engine is constrained by the Second Law of Thermodynamics, which dictates that no engine can be 100% efficient due to inevitable energy losses, primarily as waste heat.

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Related Practice

Textbook Question

The heat engine shown in FIGURE P21.62 uses 2.0 mol of a monatomic gas as the working substance.c. What is the engine's thermal efficiency?

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Textbook Question

What are (a) the heat extracted from the cold reservoir and (b) the coefficient of performance for the refrigerator shown in FIGURE EX21.21?

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Textbook Question

At what cold-reservoir temperature (in ℃) would a Carnot engine with a hot-reservoir temperature of 427℃ have an efficiency of 60%?

Textbook Question

An air conditioner removes 5.0 x 10⁵ J/min of heat from a house and exhausts 8.0 x 10⁵ J/min to the hot outdoors. What is the air conditioner's coefficient of performance?

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Textbook Question

The engine that powers a crane burns fuel at a flame temperature of 2000℃. It is cooled by 20℃ air. The crane lifts a 2000 kg steel girder 30 m upward. How much heat energy is transferred to the engine by burning fuel if the engine is 40% as efficient as a Carnot engine?

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Textbook Question

A Carnot engine whose hot-reservoir temperature is 400℃ has a thermal efficiency of 40%. By how many degrees should the temperature of the cold reservoir be decreased to raise the engine's efficiency to 60%?