Can get the solution for these physics problems? The subject is thermodynamics.

Recommended Text: Finn's Thermal Physics, third edition (CRC Press, 2017)

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_1&course_id=_53795_ Help ? 2 80% + Problem 1: Short Answers (a) Suppose that instead of measuring temperature in kelvins, physicists had all decided to use "melvins" instead. There are 50 melvins in between the freezing and boiling points of water (at standard pressure). What would the value of Boltzmann's constant be, in joules per melvin? b) In quantum mechanics, we learn that the energy levels for a single particle in a cubical box of side length L are 7212 E(nr. ny, n=) 2miz( n; + ny + n;) . (1) where m is the particle's mass and n,, ny and n, are positive integers. Verify that this quantity has units of energy. (c) Show that pressure has the same units as energy density (energy per volume) d) Deduce an approximate value of the sum 1 10 = 110 P + 210 (2) by approximationg the sum with an integral. (e) What is the ratio of the thermal de Broglie wavelengths for molecular hydrogen and molecular oxygen at room temperature? Problem 2: Helmholtz Free Energy and the Canonical Distribution We have defined the canonical distribution as P(H) = -e-BE(H) 1 (3) where B = (kBT) 1. We also know that the Helmholtz free energy is proportional to the natural log of the partition function: F = -kBT log Z . ( 4) (a) Write p(/) in terms of F instead of Z. (b) Using your answer for part (a), find log p(/) in terms of B, F and E(/). (c) Using your answer for part (b), evaluate the expectation value (- logP(A) ) = - EP(H) logP(H) . (5) Your answer should involve the expectation value for the energy, (E).2 (d) Solve for ( E). Does the result look familiar? Hint: Translate back from B to T. Problem 3: Warming Up for Quantum Mechanics Consider a system whose microstates are labeled by a number n = 0, 1, 2, 3, .... The energy of microstate /, is En = A (n+5) (6) for some constant A. (a) What is the partition function Z? It may help to recall the sum of an infinite geometric series. (b) Using (E) O log Z oB (7) evaluate (E) (c) How does your result in part (b) simplify in the limits of low temperature (B + co) and high temperature (BA small)