An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 4.2, Problem 17P
To determine
Proof of the fact that a refrigerator with COP better than the idealvalue
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Consider a van der Waal's gas that undergoes an
isothermal expansion from volume V₁ to volume V₂.
Calculate the change in the Helmholtz free energy.
2.2
(a)
(b)
From the theory of thermodynamics, with T and V
T
independent, ()₁ = T()-p. Show that the change in
internal energy is AU = a(-1/2).
Use the Maxwell distribution to calculate the average value of v2 for the molecules in an ideal gas. Check that your answer agrees with equation 6.41 (Attached).
Prove that the entropy S of an ideal gas [Sackur and Tetrode's equation] is an extensive quantity.
Then show that the entropy of the gas of particles to be separated from each other is
3
S = NKB
— Nku [2 - In (2/V)],
and that this quantity is not extensive.
Remember: by extensiveness we mean that if we scale the size of the system by a factor a (V
→ a V, N a N, but the particle density n = N/V remains constant), any extensive quantity
a s)
also scales by a factor a (here: S
→
Chapter 4 Solutions
An Introduction to Thermal Physics
Ch. 4.1 - Prob. 1PCh. 4.1 - At a power plant that produces 1 GW ( 109 watts)...Ch. 4.1 - A power plant produces 1 GW of electricity, at an...Ch. 4.1 - It has been proposed to use the thermal gradient...Ch. 4.1 - Prove directly (by calculating the heat taken in...Ch. 4.1 - To get more than an infinitesimal amount of work...Ch. 4.2 - Why must you put an air conditioner in the window...Ch. 4.2 - Can you cool off your kitchen by leaving the...Ch. 4.2 - Prob. 9PCh. 4.2 - Suppose that heat leaks into your kitchen...
Ch. 4.2 - What is the maximum possible COP for a cyclic...Ch. 4.2 - Explain why an ideal gas taken around a...Ch. 4.2 - Under many conditions, the rate at which heat...Ch. 4.2 - Prob. 14PCh. 4.2 - In an absorption refrigerator the energy driving...Ch. 4.2 - Prob. 16PCh. 4.2 - Prob. 17PCh. 4.3 - Prob. 18PCh. 4.3 - The amount of work done by each stroke of an...Ch. 4.3 - Derive a formula for the efficiency of the Diesel...Ch. 4.3 - The ingenious Stirling engine is a true heat...Ch. 4.3 - A small-scale steam engine might operate between...Ch. 4.3 - Prob. 23PCh. 4.3 - Calculate the efficiency of a Rankine cycle that...Ch. 4.3 - In a real turbine, the entropy of the steam will...Ch. 4.3 - A coal-fired power plant, with parameters similar...Ch. 4.3 - In Table 4.1, why does the entropy of water...Ch. 4.3 - Imagine that your dog has eaten the portion of...Ch. 4.4 - Liquid HFC-134a at its boiling point at 12 bars...Ch. 4.4 - Consider a household refrigerator that uses...Ch. 4.4 - Suppose that the throttling valve in the...Ch. 4.4 - Suppose you are told to design a household air...Ch. 4.4 - Prob. 33PCh. 4.4 - Consider an ideal Hampson-Linde cycle in which no...Ch. 4.4 - The magnetic field created by a dipole has a...Ch. 4.4 - Prob. 36PCh. 4.4 - A common (but imprecise) way of stating the third...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Let Ω be a new thermodynamic potential that is a “natural” function of temperature T, volume V, and the chemical potential μ. Provide a definition of Φ in the form of a Legendre transformation and also write its total differential, or derived fundamental equation, in terms of these natural variables.arrow_forwardCalculate the change in Gibbs and Helmholtz free energies for one mole of an ideal gas that undergoes a change in pressure from 2.0 bar to 1.0 bar at a constant temperature of 298.2K. Clearly show and state the partial derivative (sensitivity) in G that you need to integrate.arrow_forwardConsider N identical harmonic oscillators (as in the Einstein floor). Let the allowed energies of each oscillator (E = n h f (n = 0, 1, 2 ...)) 0, hf, 2hf and so on. A) Find the Helmholtz free energy of this system. B) Derive the expression that gives the entropy of this system as a function of temperature.arrow_forward
- Consider an ideal gas containing N atoms in a container of volume Pressure P, and absolute temperature T1 (not to be confused with K. E. T). Use the virtual theorem to derive the equation of state for a perfect gas.arrow_forwardPlease write down the proof of the Gay-Lussac-Joule experiment, i.e.for the ideal gas, u does not depend on v. Hint: you may use two-step process as shown in the figure.arrow_forward. An ideal classical gas composed of N particles, each of mass m, is enclosed in a vertical cylinder of height L placed in a uniform gravitational field (of acceleration g) and is in thermal equilibrium; ultimately, both N and L → ∞. Evaluate the partition function of the gas and derive expressions for its major thermodynamic properties. Explain why the specific heat of this system is larger than that of a corresponding system in free space.arrow_forward
- Prove that entropy is a state function.arrow_forwardANSWER PROBLEM 7.28 7.28. For the window in Problem 7.27, Calculate the transmitted and absorbed solar heat gain, using the detailed approach.arrow_forwardProblem 4.1. Recall Problem 1.34, which concerned an ideal diatomic gas taken around a rectangular cycle on a PV diagram. Suppose now that this system is used as a heat engine, to convert the heat added into mechanical work. (a) Evaluate the efficiency of this engine for the case V2 = 3V1, P2 = 2P1. (b) Calculate the efficiency of an "ideal" engine operating between the same temperature extremes.arrow_forward
- Let's consider a classical ideal gas whose single-particle partition function of molecules is Z ₁. statements is true? Which of the following Select one: a. If the gas molecules of N molecules cannot be separated from each other, and the partition function ZN of the system is written ZN = Z₁N, the entropy of the gas calculated from Z N is obtained, which is an extensive quantity. 1 O b. If the molecules cannot be separated from each other, the partition function of the system can be written in the form ZN = Z₁N/N!. In this case, the entropy calculated from Z N is obtained, which is an extensive quantity. 1 N O c. If the gas molecules of N molecules cannot be separated from each other, the partition function Z of the system can be written Z N = Z₁N.arrow_forwardConsider a large system of N indistinguishable, noninteracting molecules (perhaps in an ideal gas or a dilute solution). Find an expression for the Helmholtz free energy of this system, in terms of Z1, the partition function for a single molecule. (Use Stirling's approximation to eliminate the N!) Then use your result to find the chemical potential, again in terms of Z1.arrow_forwardConsider a monoatomic ideal gas, with Zint 1. The partition function is then 2Tm \ 3N/2 VN zmonoatomic ideal gas N! h?B Use F = -kT In Z, the Stirling approximation In N! = N In N to derive the chemical potential of the monoatomic ideal gas as a function of T, N and V. You may want to N and the appropriate partial derivative compare your result with what you got in Weekly Practice 9. (a) Take the atomic mass of Xenon to be 131 (Xenon has 8 different stable isotopes and many more metastable ones). What is the chemical potential for pure Xe gas at 1 atm and T = 300 K? Use the ideal gas law and give the answer in eV. (b) Repeat the computation from part (a) if Xe is only 1% (by number density or, equivalently, partial pressure) of a mixture of different gasses. Note: if pure Xenon is allowed to come in contact with the gas in part (b), the net flow of Xenon atoms should be into the mixture. This tells you that your answer to part (b) should be smaller than your answer to part (a).arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSON
Introduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON