Textbook Question
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?
2
views
Ch 19: Work, Heat, and the First Law of Thermodynamics
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
Not the one you use?Change textbookSelect a different textbook
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
All textbooks
Knight Calc 5th EditionCh 19: Work, Heat, and the First Law of ThermodynamicsProblem 56b
Knight Calc 5th EditionCh 19: Work, Heat, and the First Law of ThermodynamicsProblem 56bChapter 19, Problem 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?
Verified step by step guidance1
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.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
Recommended video:
Guided course
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.
Recommended video:
Guided course
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.
Recommended video:
Guided course
07:21Ideal Gases and the Ideal Gas Law
Related Practice
Textbook Question
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?
1
views
Textbook Question
An ideal-gas process is described by p=cV1/2, where c is a constant. 0.033 mol of gas at an initial temperature of 150°C is compressed, using this process, from 300 cm3 to 200 cm3. How much work is done on the gas?
1
views
Textbook Question
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. What are the gas volume and temperature after the expansion?
1
views
Textbook Question
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?
1
views
Textbook Question
A 10-cm-diameter cylinder contains argon gas at 10 atm pressure and a temperature of 50°C. A piston can slide in and out of the cylinder. The cylinder's initial length is 20 cm. 2500 J of heat are transferred to the gas, causing the gas to expand at constant pressure. What are the final length of the cylinder?