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 59a
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.
Verified step by step guidance1
Step 1: Identify the given information from the graph. At point 1, the pressure (p₁) is 400 kPa, the volume (V₁) is 2000 cm³, and the temperature (T₁) is 300 K. The process from point 1 to point 2 is adiabatic, meaning no heat is exchanged.
Step 2: Use the adiabatic relation for a diatomic gas, which is governed by the equation p₁V₁^γ = p₂V₂^γ, where γ (gamma) is the adiabatic index. For a diatomic gas, γ = 7/5. Rearrange this equation to solve for p₂.
Step 3: Determine the volume at point 2 (V₂) from the graph. From the figure, V₂ is approximately 1000 cm³. Substitute V₂, p₁, V₁, and γ into the adiabatic equation to calculate p₂.
Step 4: Use the ideal gas law, pV = nRT, to find the temperature at point 2 (T₂). Rearrange the equation to T₂ = (p₂V₂)/(nR). Substitute the values of p₂, V₂, and the gas constant R (8.314 J/mol·K) to calculate T₂. Note that n (number of moles) can be determined if additional information is provided.
Step 5: Summarize the results. You now have the pressure (p₂), volume (V₂), and temperature (T₂) at point 2. Ensure all units are consistent (e.g., convert cm³ to m³ for volume if necessary).
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 (P), volume (V), and temperature (T) of an ideal gas through the equation PV = nRT, where n is the number of moles and R is the ideal gas constant. This law is fundamental for understanding the behavior of gases under varying conditions and is essential for calculating the state variables at different points in a thermodynamic cycle.
Recommended video:
Guided course
07:21
Ideal Gases and the Ideal Gas Law
Thermodynamic Cycles
A thermodynamic cycle is a series of processes that return a system to its initial state, allowing for the analysis of energy transfer and work done. In the context of heat engines, these cycles often involve isothermal, adiabatic, isochoric, and isobaric processes, which help in understanding how energy is converted from heat to work and vice versa.
Recommended video:
Guided course
10:59The Otto Cycle
Adiabatic Process
An adiabatic process is one in which no heat is exchanged with the surroundings, meaning all changes in internal energy are due to work done on or by the system. For a diatomic gas, the relationship between pressure, volume, and temperature during an adiabatic process can be described by specific equations, which are crucial for determining the state of the gas at various points in the cycle.
Recommended video:
Guided course
06:13Entropy & Ideal Gas Processes
Related Practice
Textbook Question
A nuclear power plant generates 3000 MW of heat energy from nuclear reactions in the reactor's core. This energy is used to boil water and produce high-pressure steam at 300℃. The steam spins a turbine, which produces 1000 MW of electric power, then the steam is condensed and the water is cooled to 25℃ before starting the cycle again. What is the plant's actual 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
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
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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