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.
Ch 21: Heat Engines and Refrigerators
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 21, Problem 62a
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.
Verified step by step guidance1
Step 1: Identify the states of the gas (1, 2, and 3) from the graph. Note the pressure (p) and volume (V) values for each state. For state 1: p1 = 400 kPa, V1 = 0.050 m³; for state 2: p2 = 600 kPa, V2 = 0.025 m³; for state 3: p3 = 400 kPa, V3 = 0.025 m³.
Step 2: Use the ideal gas law, \( pV = nRT \), to calculate the temperature at each state. Rearrange the formula to \( T = \frac{pV}{nR} \), where n = 2.0 mol and R = 8.314 J/(mol·K). Substitute the values of p and V for each state into the formula.
Step 3: For state 1, substitute \( p_1 = 400 \text{ kPa} = 400 \times 10^3 \text{ Pa} \), \( V_1 = 0.050 \text{ m}^3 \), \( n = 2.0 \text{ mol} \), and \( R = 8.314 \text{ J/(mol·K)} \) into \( T_1 = \frac{p_1 V_1}{nR} \).
Step 4: For state 2, substitute \( p_2 = 600 \text{ kPa} = 600 \times 10^3 \text{ Pa} \), \( V_2 = 0.025 \text{ m}^3 \), \( n = 2.0 \text{ mol} \), and \( R = 8.314 \text{ J/(mol·K)} \) into \( T_2 = \frac{p_2 V_2}{nR} \).
Step 5: For state 3, substitute \( p_3 = 400 \text{ kPa} = 400 \times 10^3 \text{ Pa} \), \( V_3 = 0.025 \text{ m}^3 \), \( n = 2.0 \text{ mol} \), and \( R = 8.314 \text{ J/(mol·K)} \) into \( T_3 = \frac{p_3 V_3}{nR} \).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Ideal Gas Law
The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of an ideal gas through the equation PV = nRT. Here, P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. This law is fundamental for understanding the behavior of gases in various thermodynamic processes, including those in heat engines.
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Ideal Gases and the Ideal Gas Law
Thermodynamic Cycles
A thermodynamic cycle is a series of processes that involve the transfer of heat and work, returning a system to its initial state. In the context of heat engines, these cycles typically include isothermal, isochoric, isobaric, and adiabatic processes. Understanding these cycles is crucial for analyzing how heat engines operate and for calculating temperatures at different points in the cycle.
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Work Done by a Gas
The work done by a gas during expansion or compression can be calculated using the area under the pressure-volume (P-V) curve on a graph. For a heat engine, this work is a key component of its efficiency and performance. The work done is directly related to the changes in volume and pressure, making it essential for determining the temperatures at various states in the cycle.
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Related Practice
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
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
A heat engine using a diatomic gas follows the cycle shown in FIGURE P21.55. Its temperature at point 1 is 20℃. Determine Ws, Q, and ∆Eth for each of the three processes in this cycle. Display your results in a table.
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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 ∆Eth, Ws, and Q for each of the three processes.
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