Domanda del libro di testo
5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. How much heat energy is transferred to the gas to cause this expansion?
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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
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Knight Calc 5th EditionCh 19: Work, Heat, and the First Law of ThermodynamicsProblema 56b
Knight Calc 5th EditionCh 19: Work, Heat, and the First Law of ThermodynamicsProblema 56bCapitolo 19, Problema 56b
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?
Guida verificata passo dopo passo1
Step 1: Recognize that the process is isothermal, meaning the temperature remains constant throughout the expansion. For an ideal gas undergoing isothermal expansion, the work done on the gas can be calculated using the formula: \( W = -nRT \ln \left( \frac{V_2}{V_1} \right) \), where \( V_2 \) is the final volume, \( V_1 \) is the initial volume, \( n \) is the number of moles, \( R \) is the universal gas constant, and \( T \) is the temperature.
Step 2: Substitute \( V_2 = 2V_1 \) into the formula, as the problem states that the volume doubles during the expansion. This gives \( W = -nRT \ln \left( \frac{2V_1}{V_1} \right) \).
Step 3: Simplify the expression inside the logarithm. Since \( \frac{2V_1}{V_1} = 2 \), the formula becomes \( W = -nRT \ln(2) \).
Step 4: Note that the negative sign indicates that work is done by the gas on its surroundings during the expansion, as the gas is expanding against external pressure.
Step 5: Express the final formula for the work done on the gas in terms of the given variables: \( W = -nRT_1 \ln(2) \), where \( T_1 \) is the constant temperature during the isothermal process.
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Isothermal Process
An isothermal process occurs when a system's temperature remains constant while it undergoes a change in volume. For an ideal gas, this means that any heat added to the system is used to do work, rather than increasing the internal energy. The relationship between pressure, volume, and temperature is described by the ideal gas law, which is crucial for understanding how the gas behaves during expansion.
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06:13
Entropy & Ideal Gas Processes
Work Done by a Gas
The work done by a gas during expansion or compression can be calculated using the formula W = ∫ P dV, where P is the pressure and dV is the change in volume. In an isothermal expansion of an ideal gas, the work done can be expressed as W = nRT ln(Vf/Vi), where Vf and Vi are the final and initial volumes, respectively. This highlights the relationship between work, temperature, and volume changes in the gas.
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03:47Calculating Work Done on Monoatomic Gas
Ideal Gas Law
The ideal gas law, represented as PV = nRT, relates the pressure (P), volume (V), temperature (T), and number of moles (n) of an ideal gas. This law is fundamental in thermodynamics and allows for the calculation of one variable when the others are known. In the context of isothermal expansion, it helps determine how pressure changes as volume increases while maintaining a constant temperature.
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07:21Ideal Gases and the Ideal Gas Law
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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 heat energy transferred to the gas?
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