PHY 3513 Fall 1998 – Homework 9
Due at the start of class on Friday, October 30. No credit will be given for late
homework this week.
This is supposed to be an indication of the sort of questions that will appear on Exam 1. You
will be asked to solve four problems similar to these during the two-hour exam.
Answer all questions. To obtain full credit, please explain your reasoning and show all
working. Please write neatly and remember to include your name on the front page of your
answers.
1. Answer each of the following short questions.
(a) Classify each of the following thermodynamic quantities as either extensive or in-
tensive: volume, pressure, molar heat capacity at constant volume, mole number,
isothermal compressibility, molar internal energy.
(b) Which of the following fundamental equations violate(s) the Nernst postulate?
U=θ
v0
VS
Nexp(−S/NR), S= R2
v0θNVU!1/3
,S=v0
Rθ2
U2
V.
(c) Given the fundamental equation
u=Rθ h(s/R)3/2−(v/v0)5/2i,
write down three equations of state in the energy representation.
2. Nmoles of a van der Waals fluid, which obeys the equations
P+a
v2(v−b)=RT, u =cRT −
a
v,
undergo an isothermal expansion from volume V1to V2.
(a) Calculate the work done by the gas during this process.
(b) Calculate the change in internal energy during this process.
(c) Deduce the change in entropy during this process.
Your answer should be expressed solely in terms of symbols introduced above and pure
numbers (i.e., don’t define any new symbols).
3. Find the coefficient of thermal expansion αand the isothermal compressibility κTfor
the following systems:
(a) An ideal gas, which obeys Pv =RT .
(b) A non-ideal gas which obeys the Dieterici equation, P(v−b)=RT exp[−a/(vRT)].
Express all answers as functions of Tand v. Hint: Differentiate. Just do it!
