# PHY 3513 Fall 1999 – Homework 1

```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
1. For temperatures below about 2 K, the molar heat capacity of argon is well-described by
the formula
cmol = α T 3 ,
(1)
where T is the absolute temperature, and α = 2.5 mJ mol−1 K−4 .
Starting from the equation
dQ
&macr; = n cmol dT,
where n is the number of moles, find the total heat Q flowing 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. Suppose that 10 g of ice initially at −20 ◦ C is dropped into 20 g 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?
of which are physically nonsensical): “30 g of ice at −30 ◦ C,” “5 g of ice at −20 ◦ C plus 25 g
of water at 5 ◦ C,” and “20 g of water and 20 g of steam, both at 100 ◦ C.”
Data: cice = 2220 J kg−1 K−1 , cwater = 4190 J kg−1 K−1 , csteam = 1520 J kg−1 K−1 ,
LF = 333 kJ kg−1 , LV = 2256 kJ kg−1 .
3. The pressure P , the molar volume v, and the temperature T of a certain gas are related
by the equation of state
a
P (v − b) +
= R T.
(2)
Tv
Here a, b, and R are positive constants.
Consider n moles of the gas sealed inside a cylinder with a movable piston. Calculate the
total work done by the gas on expanding from volume V1 to V2 &gt; V1 when 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 , a constant.
(c) Isochoric: V = V1 = V2 .
(d) Arbitrary: T = c(v − b), where c is a constant.
Hints: (i) Don’t confuse the volume V with 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)].
```