Domanda del libro di testo
An ideal-gas process is described by p=cV1/2, where c is a constant. Find an expression for the work done on the gas in this process as the volume changes from V1 to V2.
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Ch 19: Work, Heat, and the First Law of Thermodynamics
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- 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: 9780137344796Non è quello che usi tu?Cambia libro di testo
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Knight Calc 5th EditionCh 19: Work, Heat, and the First Law of ThermodynamicsProblema 56a
Knight Calc 5th EditionCh 19: Work, Heat, and the First Law of ThermodynamicsProblema 56aCapitolo 19, Problema 56a
n moles of an ideal gas at temperature T1 and volume V1 expand isothermally until the volume has doubled. In terms of n, T1, and V1, what is the final temperature?
Guida verificata passo dopo passo1
Step 1: Recognize that the process described is isothermal, meaning the temperature of the gas remains constant throughout the expansion. Therefore, the final temperature T₂ is equal to the initial temperature T₁.
Step 2: Recall the ideal gas law, which is given by the equation: , where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.
Step 3: Since the temperature remains constant (T₁ = T₂), the product of pressure and volume (P × V) must also remain constant during the isothermal process. This is expressed as: .
Step 4: In this problem, the volume doubles, so . Substituting this into the equation for isothermal processes, we find that the pressure must adjust accordingly to maintain the equality.
Step 5: Conclude that the final temperature T₂ is the same as the initial temperature T₁, as the isothermal condition ensures no change in temperature. Thus, T₂ = T₁.
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Ideal Gas Law
The Ideal Gas Law is a fundamental equation in thermodynamics that relates the pressure, volume, temperature, and number of moles of an ideal gas. It is expressed as PV = nRT, where 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 crucial for understanding the behavior of gases under various conditions.
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07:21
Ideal Gases and the Ideal Gas Law
Isothermal Process
An isothermal process is a thermodynamic process that occurs at a constant temperature. For an ideal gas, this means that any expansion or compression of the gas occurs without a change in temperature, which implies that heat is exchanged with the surroundings to maintain thermal equilibrium. This concept is essential for analyzing the behavior of gases during expansion or compression.
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06:13Entropy & Ideal Gas Processes
Doubling Volume in Isothermal Expansion
When an ideal gas undergoes isothermal expansion and its volume doubles, the pressure of the gas decreases according to Boyle's Law, which states that pressure is inversely proportional to volume at constant temperature. In this scenario, since the temperature remains constant, the final state of the gas can be analyzed using the Ideal Gas Law to determine how the pressure and other properties change as the volume increases.
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05:21Volume Thermal Expansion
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n moles of an ideal gas at temperature T1 and volume V1 expand isothermally until the volume has doubled. In terms of n, T1, and V1, what are the work done on the gas?
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