Question

CH 3310 Physical Chemistry Homework 10 Due 11:15 a.m. Fri. 1 Nov. 2019 P=kt On Q Problem 1: Thermodynamic Connection Formula for Enthalpy (2 points) Equations (1) and (2) provide thermodynamic connection formulas for calculating U and P from the partition function. Use these equations, plus the definition of the enthalpy, to derive a thermodynamic connection formula for H. (Hint: Don't overcomplicate this problem. It requires very little work. I'm assigning it mainly so that you have seen this thermo connection formula, and will be able to calculate H from Q in the future.) m u li Ponce Anoints)

Answer 1

Enthalpy: It is a thermodynamic quantity equivalent to the total heat content of a system.

Enthalpy(H) is equal to the internal energy(U) of the system plus the product of pressure and volume(PV).

$H= U+ PV$

In this problem, we have given that

$U= kT^{2}[\frac{\partial Q}{\partial T}]_{V}$ and

$P= kT[\frac{\partial Q}{\partial V}]_{T}$,

$\Rightarrow H = kT^{2}[ \frac{\partial Q}{\partial T}]_{V} + kT[ \frac{\partial Q}{\partial V}]_{T} \times V$

In case of an ideal gas, using Ideal gas equation, $PV= nRT$

$V=\frac{nRT}{P}$

$V=\frac{nRT}{kT[\frac{\partial Q}{\partial V}]_{T}}$

By putting all these values in enthalpy equation,

$H=U + PV$

$H= U + P \times \frac{nRT}{P}$

$H= U + nRT$

$H = kT^{2}[ \frac{\partial Q}{\partial T}]_{V} + nRT$

Here, k is the boltzmann constant and R is universal gas constant, both are related by equation, $R = N_{A}\times K$ , where N_A is Avogadro constant or number.