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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
All textbooksKnight Calc 5th EditionCh 21: Heat Engines and RefrigeratorsProblem 62b
Chapter 21, Problem 62b

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 ∆Eth, Ws, and Q for each of the three processes.

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Step 1: Understand the problem. The heat engine operates with 2.0 mol of a monatomic gas, and we need to calculate the change in internal energy (∆Eₜₕ), work done (Wₛ), and heat transfer (Q) for each of the three processes. Recall that for a monatomic gas, the internal energy is related to temperature through the formula: E=32nRT, where n is the number of moles, R is the gas constant, and T is the temperature.
Step 2: Identify the type of processes involved. Heat engines typically involve processes such as isothermal (constant temperature), adiabatic (no heat transfer), or isochoric (constant volume). For each process, use the appropriate thermodynamic relationships to calculate ∆Eₜₕ, Wₛ, and Q. For example: Q=W for isothermal processes, and ∆Eₜₕ=Q-W for general processes.
Step 3: Use the first law of thermodynamics, ∆Eₜₕ=Q-W, to calculate the change in internal energy for each process. For a monatomic gas, the change in internal energy depends only on the change in temperature. If the temperature remains constant (isothermal process), then ∆Eₜₕ=0. For adiabatic processes, Q=0, and the work done is equal to the change in internal energy.
Step 4: Calculate the work done (Wₛ) for each process. For isothermal processes, use the formula: W=nRTln(VfVi), where Vₓ represents the initial and final volumes. For adiabatic processes, use the relationship between pressure, volume, and temperature for adiabatic expansion/compression.
Step 5: Summarize the results in a table format. For each process, list the values of ∆Eₜₕ, Wₛ, and Q based on the calculations performed in the previous steps. Ensure that the values are consistent with the type of process (isothermal, adiabatic, or isochoric) and the given conditions of the heat engine.

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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 states that energy cannot be created or destroyed, only transformed from one form to another. In the context of a heat engine, this principle is crucial for understanding how heat energy (Q) is converted into work (W) and how internal energy (∆E) changes during the engine's cycles.
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The First Law of Thermodynamics

Monatomic Gas Properties

Monatomic gases, such as helium or argon, consist of single atoms and exhibit specific thermodynamic behaviors. Their internal energy is directly related to temperature and can be calculated using the formula U = (3/2)nRT, where n is the number of moles, R is the gas constant, and T is the temperature in Kelvin. Understanding these properties is essential for analyzing the energy changes in the heat engine.
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Thermodynamic Processes

Thermodynamic processes describe the changes in state variables of a system, such as pressure, volume, and temperature, during energy transfer. In a heat engine, these processes can be isothermal, adiabatic, isochoric, or isobaric, each affecting the work done (W) and heat exchanged (Q) differently. A clear understanding of these processes is necessary to construct the required table of energy changes.
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Related Practice
Textbook Question

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.

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

FIGURE P21.57 shows the cycle for a heat engine that uses a gas having γ = 1.25. The initial temperature is T1 = 300 K, and this engine operates at 20 cycles per second. What is the power output of the engine?

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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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