PHYSICS 313
Problem set 5 2003
Given NOV. 7 2003
Due NOV 17 2003

Problem 1:
a: Show that for a system with control variables $V,N,T$

$$\left(\frac{\partial S}{\partial V}\right)_{T,N}=\left(\frac{\partial P}{\partial T}\right)_{V,N}$$

b: Show that for a system determined by $P,T,N$

$$\left(\frac{\partial S}{\partial P}\right)_{T,N}=-\left(\frac{\partial V}{\partial T}\right)_{P,N}$$

Problem 2:
Sprinkle some pepper on the surface of water in a bowl. Then touch the middle of surface with a bar of soap. What happens? Speculate why.
Problem 3:
a: The critical values of the temperature, pressure and volume for a van der Waals gas are

$$V_c=3Nb;\;\;P_c=\frac{a}{27b^2};\;\;k_BT_c=\frac{8a}{27b}$$

For water is $T_c=374\; ^o$C and $P_c=221$ bar. Use this result to determine the constants $a$ and $b$.
b: Draw the $T=100\; ^0$C isotherm were water a van der Waals fluid.
c: How far off is the predicted value of the boiling point of water?