Question 2.166: A gas of interacting atoms has an equation of state and heat...
A gas of interacting atoms has an equation of state and heat capacity at constant volume given by the expressions
p(T, V)=a T^{1 / 2}+b T^{3}+c V^{-2}C_{v}(T, V)=d T^{1 / 2} V+e T^{2} V+f T^{1 / 2},
where a through f are constants which are independent of T and V.
(a) Find the differential of the internal energy dU(T,V )in terms of dT and dV.
(b) Find the relationships among a through f due to the fact that U(T,V) is a state variable.
(c) Find U(T,V) as a function of T and V.
(d) Use kinetic arguments to derive a simple relation between p and U for an ideal monatomic gas (a gas with no interactions between the atoms, but whose velocity distribution is arbitrary). If the gas discussed in the previous parts were to be made ideal, what would be the restrictions on the constants a through f?
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