Problem Set #24: Fundamental Thermodynamic Relations

University:
The Pennsylvania State University
Course:
CHEM 450 | Thermodynamics
Academic year:

2024
Views:

465

Pages:

2
Author:

Alexis H.

Problem Set #24 Assigned: Feb. 28, 2024 Due: March 1, 2024 at 2:30 pm 1. Starting from: dG = dH – d(TS), we derived the fundamental equation of chemical thermodynamics, dG = Vdp – SdT. Its natural variables are pressure and temperature. (a) Please derive an equivalent exact differential for dA starting from dA = dU – d(TS) (b) What are the natural variables of your new expression? 2. Derive the Maxwell relation corresponding to the exact differential you found in (1). 3. Use the new Maxwell relationship that you found to demonstrate that the entropy of a perfect gas is linearly dependent on ln V, that is S = a + bln(V). 4. (a) Use the appropriate Maxwell relation to show how the entropy of a perfect gas varies with volume at constant temperature. (b) Use the same Maxwell relation to show how the entropy of a van der Waals gas varies with volume at constant temperature. (c) Which of the two showed the greater change in entropy? How can this result be understood? 1 dA Tds Pdr d TS Tds 2 dA pdr Sdt dA do dTS a Tai d dA pdV Sdt IT b thenaturalvariables are nowpressurevolume temperature entropy and 3 dA pdr Sdt av an MT N MR S a b Inv 88 Idt AV atblnV dT at binv at a binv dt 4 a 27 Jun Yum p RI Vm Finn Emt d Em dum 8h high Δ5 dum RSim dum f III E E I s TED ΔS b Pmnb ΔS RSVhnb ΔS Rln Vm nb (c) The one in a would have the higher entropy because the second one is subtracted by the number of moles as well as the coe cient while the rst one is the volume alone