PHYSICS 313
Problem set 3 2003
Given Oct. 8 2003
Due Oct 17 2003

Problem 1:
Argon is a monatomic ideal gas with molecular weight 39.95 g mol$^{-1}$.
a: Calculate the entropy of 1 mol of argon at 300 K and pressure 1 bar.
b:The gas in a: is heated to 600 K at constant pressure. What is the change in entropy?
c: The gas in a: is expanded adiabatically until its volume is doubled. What is the change in entropy?
Problem 2:
The outcome of $N$ tosses of a fair coin is $H$ heads and $T=H-m=N-H$. The probability of the difference $m$ between the number of heads and tails is to a good approximation a Gaussian with mean $\langle m\rangle =0$ and variance $N$. a: What is the entropy associated with outcomes $m=0$ if $N=10^6$?
b; What is the entropy in the two cases for the outcome $m=100$, $N=10^6$?
Problem 3:
1 kg of aluminum at 400 K is dunked into 1 kg of water at 300K. Assume that no heat is lost to the outside, that Al is an Einstein solid with atomic weight 27 g mol$^-1$, with an Einstein temperature much less that 300 K, and that the specific heat of water is 1 cal g$^{-1}$
a: What is the final temperature?
b: What is the change in entropy of the water?
c: What is the change in entropy of the aluminum?