PHY 3513 Fall 1998 – Homework 1
Due at the start of class on Wednesday, September 2.
Answer all questions. You must explain your reasoning and show all working to obtain the
maximum possible marks. Please write neatly and remember to include your name on the
front page of your answers.
1. As mentioned in class, the molar heat capacity cmol of most substances approaches a
universal constant value at high temperatures. At low temperatures, however, cmol varies
greatly from material to material, and is also temperature dependent. For many metals, the
molar heat capacity is well-described by the low-temperature form
cmol =γT +αT3,(1)
where Tis the absolute temperature; both γand αdepend on the metal in question.
Starting from the equation
¯dQ =nc
mol dT,
where nis the number of moles, find the total heat Qwhen 0.4 mol of a metal described by
Eq. (1) is cooled from 40 K to 10 K. Take γ=1.0mJmol
−1K−2and α=0.2mJmol
−1K−4.
2. Supp ose that 10 g of ice initially at −20 ◦C is brought into thermal contact with 1g
of superheated steam initially at 116 ◦C. Assuming that the combined ice-steam system
is closed (i.e., no material or heat crosses its boundaries and no work is done by/on the
system), what is the final equilibrium state? Express your final answer in roughly the same
format as the following sample answers (all of which are physically nonsensical): “16g of ice
at −30 ◦C,” “4 g of ice at −5◦C and 7 g of steam at 103 ◦C,” and “8 g of water and 5 g of
steam, both at 100 ◦C.”
Data: cice = 2220 J kg−1K−1,cwater = 4190 J kg−1K−1,csteam = 1520 J kg−1K−1,
LF= 333 J kg−1,LV= 2256 J kg−1.
3. A certain sample of gas closed in a cylinder obeys the so-called van der Waals equation
relating its pressure P,volumeVand temperature T:
P+a
V2(V−b)=cT. (2)
Here a,b,andcare positive constants.
Calculate the total work done by the gas on expanding from volume V1to V2>V
1when
the expansion is performed in each of four different ways specified by the various constraints
specified in (a)–(d) below.
(a) Isothermal: T=T0, a constant.
(b) Isobaric: P=P0,aconstant.
(c) Isochoric: V=V1=V2.
(d) Arbitrary: T=d(V−b).