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 63b

Chapter 21, Problem 63b

The heat engine shown in FIGURE P21.63 uses 0.020 mol of a diatomic gas as the working substance. Make a table that shows ∆E_th, W_s, and Q for each of the three processes.

Name: Physics for Scientists and Engineers
Author: Knight Calc
ISBN: 9780137344796

Verified step by step guidance

Step 1: Identify the three processes in the heat engine cycle from the graph. The processes are: (1 → 2) adiabatic compression, (2 → 3) isobaric expansion, and (3 → 1) isochoric cooling.

Step 2: For each process, calculate the change in internal energy (∆Eth) using the formula ∆Eth = n * Cv * ∆T, where n is the number of moles, Cv is the molar specific heat at constant volume for a diatomic gas, and ∆T is the change in temperature. Use the ideal gas law (PV = nRT) to find temperatures at each state.

Step 3: Calculate the work done (Ws) for each process. For the adiabatic process (1 → 2), use the formula Ws = (P2 * V2 - P1 * V1) / (γ - 1), where γ = Cp/Cv. For the isobaric process (2 → 3), use Ws = P * ∆V. For the isochoric process (3 → 1), Ws = 0 since volume does not change.

Step 4: Calculate the heat transfer (Q) for each process using the first law of thermodynamics: Q = ∆Eth + Ws. For the adiabatic process (1 → 2), Q = 0 since no heat is exchanged. For the isobaric and isochoric processes, use the calculated values of ∆Eth and Ws.

Step 5: Organize the results into a table with columns for each process (1 → 2, 2 → 3, 3 → 1) and rows for ∆Eth, Ws, and Q. Ensure all values are consistent with the calculations and the graph provided.

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 states that energy cannot be created or destroyed, only transformed from one form to another. In the context of a heat engine, this principle relates the change in internal energy (∆E_th) to the work done by the system (W_s) and the heat added to the system (Q) through the equation ∆E_th = Q - W_s.

Heat Transfer (Q)

Heat transfer (Q) refers to the energy exchanged between the system and its surroundings due to a temperature difference. In a heat engine, Q is the heat absorbed from the hot reservoir during the heating process, which is essential for performing work and changing the internal energy of the gas.

Work Done by the System (W_s)

Work done by the system (W_s) is the energy transferred when the gas expands or compresses against an external pressure. In the context of the heat engine cycle shown in the diagram, W_s can be calculated during the expansion and compression processes, which are critical for understanding the engine's efficiency and performance.

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Textbook Question

A heat engine uses a diatomic gas that follows the pV cycle in FIGURE P21.59. Determine the pressure, volume, and temperature at point 2.

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Textbook Question

A heat engine with 0.20 mol of a monatomic ideal gas initially fills a 2000 cm³ cylinder at 600 K. The gas goes through the following closed cycle: Isothermal expansion to 4000 cm³. Isochoric cooling to 300 K. Isothermal compression to 2000 cm³. Isochoric heating to 600 K. How much work does this engine do per cycle and what is its thermal efficiency?

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Textbook Question

100 mL of water at 15℃ is placed in the freezer compartment of a refrigerator with a coefficient of performance of 4.0. How much heat energy is exhausted into the room as the water is changed to ice at -15℃?

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Textbook Question

The heat engine shown in FIGURE P21.62 uses 2.0 mol of a monatomic gas as the working substance. Determine T₁, T₂ and T₃.

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Textbook Question

FIGURE CP21.70 shows two insulated compartments separated by a thin wall. The left side contains 0.060 mol of helium at an initial temperature of 600 K and the right side contains 0.030 mol of helium at an initial temperature of 300 K. The compartment on the right is attached to a vertical cylinder, above which the air pressure is 1.0 atm. A 10-cm-diameter, 2.0 kg piston can slide without friction up and down the cylinder. Neither the cylinder diameter nor the volumes of the compartments are known. How much heat is transferred from the left side to the right side?

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Textbook Question

The heat engine shown in FIGURE P21.62 uses 2.0 mol of a monatomic gas as the working substance. Make a table that shows ∆E_th, W_s, and Q for each of the three processes.

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The heat engine shown in FIGURE P21.63 uses 0.020 mol of a diatomic gas as the working substance. Make a table that shows ∆Eth, Ws, and Q for each of the three processes.

Key Concepts

First Law of Thermodynamics

Heat Transfer (Q)

Work Done by the System (W_s)

The heat engine shown in FIGURE P21.63 uses 0.020 mol of a diatomic gas as the working substance. Make a table that shows ∆E_th, W_s, and Q for each of the three processes.