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

2024
Views:

140

Pages:

2
Author:

Alexis H.

Problem Set #15 Assigned: February 9, 2024 Due: Feb. 12, 2024 at 2:30 pm 1. Use the equipartition theorem to estimate the values of = Cp,m/Cv,m for NH3 and CH4. Make these estimates both with and without taking the vibrational contributions into account. Experimentally, it has been measured that Cp,m=35.31 J/mol K for methane at 298 K, while Cp,m = 37.0 for ammonium. Please comment on how close your equipartition estimates were. Note: Each atom in a molecule contributes 3 degrees of freedom (or modes). However, vibrational modes count twice (kinetic & potential energy) toward the heat capacity. 2. Calculate Tf for a sample of Ar of mass 12.0 g that is expanded in an adiabatic, reversible manner from 1.00 L at 273.15 K to 3.00 L. 3. A sample consisting of 1.00 mol of perfect gas with Cv = 20.8 J/K is initially at 4.25 atm and 300 K. It undergoes reversible adiabatic expansion until its pressure reaches 2.50 atm. Find Vf, Tf, and the amount of work, w, that was done. 4. Calculate the final temperature, work done, and change in internal energy when 1.00 mol NH3(g) at 298 K is used in a reversible adiabatic expansion from 0.50 L to 2.00 L. 1 w ovibrations CH Gm m Cv.m w 3 E R 3E R GM ZR z Crim 24.942 Cvm 74.826 3 44 1 1.30 i a 1.33 wovibrations NH p.m 3 E R 3E R ER ER Cvm 9R 3R 35.31 35.31 8.314 vibrations 1.11 w vibrations CV.me ER RtZRt6 Cv.m Cv 9R Gm m 37 1.314 cam 1942 7 1.29 2334924526 1 1.33 Cvm 74.826 X 749 2 1.11 The experimental value is less than the one without vibrations and greater than the one with vibrations for both OR E Y Tz T Y 2 1 a 3k KR 1273 I 273 I 131.24k 8.314 20.8 3 Y 20.8 1.4 PV NRT V PV NRT BT Tf 1m01 0.08201 300k V pV Tf 2.50 v I 4 1 IV a 298 0.5 4 8.5L 4 Y TV 257.9k p V2 4.25 5 8 4 V2 W I 4.25 5.8L 1.33 U Q W T 2 act t T 187.7k 00 2.1 4 W 314187.7298 w 2.750.4J NCr Tz T 1m01 20.8 258 300 873.6J