An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter 5.2, Problem 20P
To determine
To find:At what temperature Helmholtz free energy of a hydrogen atom in the first excited level is positive and negative.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Show that the entropy of a two-state paramagnet, expressed asa function of temperature, is S = Nk [ln(2coshx) -x tanh x], where x = µB/kT.Check that this formula has the expected behavior as T → 0 and T → ∞ .
For a gas trapped in a two-dimensional harmonic oscillator, E = hf (nx+ny),
sketch the positions of states in the n-plane and draw a couple of curves of
constant energy. Calculate U/N at T = 0 and express it as a multiple of the
Fermi energy. What is the density of states?
Why is the entropy higher for a system with 5 particles with energy states >1 than for a system with 5 particles with energy states less than or equal to 1?
Chapter 5 Solutions
An Introduction to Thermal Physics
Ch. 5.1 - Prob. 1PCh. 5.1 - Consider the production of ammonia from nitrogen...Ch. 5.1 - Prob. 3PCh. 5.1 - Prob. 4PCh. 5.1 - Consider a fuel cell that uses methane (natural...Ch. 5.1 - Prob. 6PCh. 5.1 - The metabolism of a glucose molecule (see previous...Ch. 5.1 - Derive the thermodynamic identity for G (equation...Ch. 5.1 - Sketch a qualitatively accurate graph of G vs. T...Ch. 5.1 - Suppose you have a mole of water at 25C and...
Ch. 5.1 - Suppose that a hydrogen fuel cell, as described in...Ch. 5.1 - Prob. 12PCh. 5.1 - Prob. 13PCh. 5.1 - Prob. 14PCh. 5.1 - Prob. 15PCh. 5.1 - Prob. 16PCh. 5.1 - Prob. 17PCh. 5.2 - Prob. 18PCh. 5.2 - In the previous section 1 derived the formula...Ch. 5.2 - Prob. 20PCh. 5.2 - Is heat capacity (C) extensive or intensive? What...Ch. 5.2 - Prob. 22PCh. 5.2 - Prob. 23PCh. 5.3 - Go through the arithmetic to verify that diamond...Ch. 5.3 - Prob. 25PCh. 5.3 - How can diamond ever be more stable than graphite,...Ch. 5.3 - Prob. 27PCh. 5.3 - Calcium carbonate, CaCO3, has two common...Ch. 5.3 - Aluminum silicate, Al2SiO5, has three different...Ch. 5.3 - Sketch qualitatively accurate graphs of G vs. T...Ch. 5.3 - Sketch qualitatively accurate graphs of G vs. P...Ch. 5.3 - The density of ice is 917kg/m3. (a) Use the...Ch. 5.3 - An inventor proposes to make a heat engine using...Ch. 5.3 - Below 0.3 K the Slope of the 3He solid–liquid...Ch. 5.3 - Prob. 35PCh. 5.3 - Effect of altitude on boiling water. (a) Use the...Ch. 5.3 - Prob. 37PCh. 5.3 - Prob. 38PCh. 5.3 - Prob. 39PCh. 5.3 - The methods of this section can also be applied to...Ch. 5.3 - Suppose you have a liquid (say, water) in...Ch. 5.3 - Ordinarily, the partial pressure of water vapor in...Ch. 5.3 - Assume that the air you exhale is at 35C, with a...Ch. 5.3 - Prob. 44PCh. 5.3 - Prob. 46PCh. 5.3 - Prob. 47PCh. 5.3 - Prob. 48PCh. 5.3 - Prob. 49PCh. 5.3 - The compression factor of a fluid is defined as...Ch. 5.3 - Prob. 51PCh. 5.3 - Prob. 52PCh. 5.3 - Repeat the preceding problem for T/Tc=0.8.Ch. 5.3 - Prob. 54PCh. 5.3 - Prob. 55PCh. 5.4 - Prove that the entropy of mixing of an ideal...Ch. 5.4 - In this problem you will model the mixing energy...Ch. 5.4 - Suppose you cool a mixture of 50% nitrogen and 50%...Ch. 5.4 - Suppose you start with a liquid mixture of 60%...Ch. 5.4 - Suppose you need a tank of oxygen that is 95%...Ch. 5.4 - Prob. 62PCh. 5.4 - Everything in this section assumes that the total...Ch. 5.4 - Figure 5.32 shows the phase diagram of plagioclase...Ch. 5.4 - Prob. 65PCh. 5.4 - Prob. 66PCh. 5.4 - Prob. 67PCh. 5.4 - Plumbers solder is composed of 67% lead and 33%...Ch. 5.4 - What happens when you spread salt crystals over an...Ch. 5.4 - What happens when you add salt to the ice bath in...Ch. 5.4 - Figure 5.35 (left) shows the free energy curves at...Ch. 5.4 - Repeat the previous problem for the diagram in...Ch. 5.5 - If expression 5.68 is correct, it must be...Ch. 5.5 - Prob. 74PCh. 5.5 - Compare expression 5.68 for the Gibbs free energy...Ch. 5.5 - Seawater has a salinity of 3.5%, meaning that if...Ch. 5.5 - Osmotic pressure measurements can be used to...Ch. 5.5 - Because osmotic pressures can be quite large, you...Ch. 5.5 - Most pasta recipes instruct you to add a teaspoon...Ch. 5.5 - Use the Clausius–Clapeyron relation to derive...Ch. 5.5 - Prob. 81PCh. 5.5 - Use the result of the previous problem to...Ch. 5.6 - Prob. 83PCh. 5.6 - Prob. 84PCh. 5.6 - Prob. 85PCh. 5.6 - Prob. 86PCh. 5.6 - Sulfuric acid, H2SO4, readily dissociates into H+...Ch. 5.6 - Prob. 88PCh. 5.6 - Prob. 89PCh. 5.6 - When solid quartz dissolves in water, it combines...Ch. 5.6 - When carbon dioxide dissolves in water,...Ch. 5.6 - Prob. 92P
Knowledge Booster
Similar questions
- Consider a system consisting of a single hydrogen atom/ion, which has two possible states: unoccupied (i.e., no electron present) and occupied (i.e., one electron present, in the ground state). Calculate the ratio of the probabilities of these two states, to obtain the Saha equation, already derived. Treat the electrons as a monatomic ideal gas, for the purpose of determining J-l. Neglect the fact that an electron has two independent spin states.arrow_forwardIf levels 1 and 2 are separated by an energy E2 – E1 such that the corresponding transition frequency falls in the middle of the visible range, calculate the ratio of the populations of the two levels in thermal equilibrium at room temperature and hence interpret the results physically?arrow_forwardConsider two isolated systems of noninteracting spins with Na=4 and Nb= 16. Their initial energies are Ea= -2uB and Eb= -2ub. (a) What is the total number of microstates available to the composite system?(SOLVED) (b) If the two systems are now allowed to exchange energy with one another, what is the probability that system A has energy Ea?(SOLVED) (c) What is the mean value of Ea and its relative fluctuations? Calculate the analogous quantities for system B.(SOLVED) (d) What is the most probable macrostate for the composite system? (Help pls)arrow_forward
- Consider a free Fermi gas in two dimensions, confined to a squarearea A = L2. Because g(€) is a constant for this system, it is possible to carry out the integral 7.53 for the number of particles analytically. Do so, and solve for μ as a function of N. Show that the resulting formula has the expected qualitative behavior.arrow_forwardCalculate the number of microstates that are available in a single atom of carbon in graphite.The standard molar entropy (S°) of carbon is 5.7 J/(mol · K) and the Boltzmann constant (kB) is1.381 × 10 ―23?/?. HELP PLEASEarrow_forwardSuppose you flip a quarter 10 times. Find the approximate entropy (using Stirling's approximation) divided by the Boltzmann constant ?/?.arrow_forward
- P2D.8 Use the fact that (∂U/∂V)T = a/Vm2for a van der Waals gas (Topic 1C)to show that μCp,m ≈ (2a/RT) − b by using the definition of μ and appropriaterelations between partial derivatives. Hint: Use the approximation pVm ≈ RTwhen it is justifiable to do so.arrow_forwardThe volume of a monatomic ideal gas triples in an isothermalexpansion. By what factor does its pressure change?arrow_forwardProblem 7.3. Consider a system consisting of a single hydrogen atom/ion, which has two possible states: unoccupied (i.e., no electron present) and occupied (i.e., one electron present, in the ground state). Calculate the ratio of the probabilities of these two states, to obtain the Saha equation, already derived in Section 5.6. Treat the electrons as a monatomic ideal gas, for the purpose of determining J-arrow_forward
- For a certain metal the stiffness of the interatomic bond and the mass of one atom are such that the spacing of the quantum oscillator energy levels is 8.0e-23 J. A nanoparticle of this metal consisting of 8 atoms has a total thermal energy of 112e-23 J. What is the entropy of this nanoparticle?arrow_forwardFor a system of fermions at room temperature, compute the probability of a single-particle state being occupied if its energy is. 1 eV less than μarrow_forwardLet p(x, y) be the joint probability distribution of the two random variables X and Y. Define the conditional entropy H(X | Y ) in terms of the joint distribution and associated conditional probabilities.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning