PHY 3513 Fall 1999 – Homework 1
Due at the start of class on Friday, September 3.
Answer all questions. To obtain full credit, you must explain your reasoning and show all
working. Please write neatly and include your name on the front page of your answers.
1. For temperatures below about 2 K, the molar heat capacity of argon is well-described by
the formula
cmol =αT3,(1)
where Tis the absolute temperature, and α= 2.5 mJ mol−1K−4.
Starting from the equation
¯dQ =nc
mol dT,
where nis the number of moles, find the total heat Qflowing into 0.065 mol of argon when
it is first heated from 1.30 K to 1.90 K, then cooled to 0.80 K.
2. Supp ose that 10 g of ice initially at −20 ◦C is dropped into 20g of water initially at 5 ◦C.
Assuming that the combined ice-water 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): “30 g of ice at −30 ◦C,” “5 g of ice at −20 ◦Cplus25g
ofwaterat5
◦C,” and “20 g of water and 20 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 kJ kg−1,LV= 2256 kJ kg−1.
3. The pressure P, the molar volume v, and the temperature Tof a certain gas are related
by the equation of state
P(v−b)+ a
Tv =RT. (2)
Here a,b,andRare positive constants.
Consider nmoles of the gas sealed inside a cylinder with a movable piston. 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=c(v−b), where cis a constant.
Hints: (i) Don’t confuse the volume Vwith the molar volume v=V/n. (ii) There are a
couple of places where it will be useful to use partial fractions to re-express 1/[v(v−b)].