PHYSICS 313
Problem set 4 2002
Given Oct 7
Due Oct 16

Problem 1: Use the Sackur-Tetrode formula

$$S=Nk_B\left(\ln(\frac{V}{Nv_q})+\frac{5}{2}\right)$$

$$v_q=\left(\frac{h^2}{2\pi mk_BT}\right)^{3/2}$$

to estimate for which temperature the entropy would turn negative in a monatomic ideal gas with the atomic mass of He$_4$ at a pressure of 1 bar?
Problem 2: Verify using the Sackur-Tetrode formula that the entropy of a monatomic ideal gas stays constant under an adiabatic expansion

$$P_fV_f^\gamma=P_iV_i^\gamma$$

if $\gamma=5/3$.
Problem 3:. Assume that the entropy of a diatomic ideal gas is of the form of the Sackur Tetrode formula, but with

$$v_q=constant\; T^{-\alpha}$$

where the constant depends on molecular properties, and natural constants such as $h,\;\pi,\; etc$ but not on the thermodynamic variables $V,T,N$. What is the value of $\alpha$ if

$$\gamma=\frac{C_P}{C_V}=1.4$$