Consider the following two virial equations of state.  Z = 1 + 2B’ p + 3 C’ p2 + D’ p3 + E’ p4 + ….. Z = 1 + 4B (1/Vm) + 5C (1/Vm)2 + D (1/Vm)3 + E (1/Vm)4+ …. where B’, B, C’, C, D’, D, E’ and E, etc, are virial coefficients; p is the pressure and Vm is the molar volume. (a) Find the relation between B and B’. (b) Determine the ratio B’/B at T = 420 K from your expression including the appropriate units in your answer.

A2. Determine total differentials: dT = dT(s,v), dP = dP(s, v), dụ = dµ(s,v). %|

The Maxwell speed distribution function is given by: ƒ(v) = 3 m (2 KT)² 4πv² e-mv²/2kBT i. Show that the average speed of the molecule is given by (v) = /8kgT/πm. A valve connecting a first chamber, containing a mixture of 10% ³He and 90% *He, is opened to a second chamber, which is under vacuum. The diameter of the valve is small compared to the mean free path of the atoms, and the number of atoms escaping from the first to the second chamber will depend on the species. ii. iii. Calculate the ratio of the number of ³He and 4He atoms that have escaped the first chamber. How many times, approximately, does this procedure need to be repeated to produce a mixture of 30% ³He? [Hint: Use the flux Ⓡ = n(v) where n is the number density n = =N/V]

_= = P +T (5) v Given that the internal pressure of a gas is defined as. SV T value of the internal pressure of a perfect gas? O RT V-b V OR 00 ; What is the