ChronicQuantumAddict
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1. Show that for an ideal gas
2. The Helmholtz function of a certain gas is:
For this one i need the answer verified, i think i have it right. We know that -P = (\frac{(\delta(F))}{(\delta(V))})_T, and thus all i have to do is differentiate the negative of the above function for F with respect to V, and the J(T) function disappears.
3. The Gibbs function of a certain gas is:
Now, the answer in the book is:
a).f = c_v(T-T_0)-c_vT\ln(T/T_0)-RT\ln(v/v_0)-s_0T
b).g = c_p(T-T_0)-c_pT\ln(T/T_0)+RT\ln(P/P_0)-S_0T
totally lost here, where do i begin?b).g = c_p(T-T_0)-c_pT\ln(T/T_0)+RT\ln(P/P_0)-S_0T
2. The Helmholtz function of a certain gas is:
F = -\frac{n^2a}{V} - nRT \ln(V-nb) + J(T),
where J is a function of T only. Derive an expression for the pressure.For this one i need the answer verified, i think i have it right. We know that -P = (\frac{(\delta(F))}{(\delta(V))})_T, and thus all i have to do is differentiate the negative of the above function for F with respect to V, and the J(T) function disappears.
3. The Gibbs function of a certain gas is:
G = nRT\ln(P) + A + BP + \frac{CP^2}{2} + \frac{DP^3}{3}(
where A,B,C, and D are constants. Find the equation of state of the gas.Now, the answer in the book is:
nRT + BP + CP^2 + DP^3
the only way i see to get this is to differentiate the expression for with respect to P, giving:\frac{nRT}{P} + B + CP + DP^2
and then multiplying this result through by P, or in other words, the equation of state is given by:P(\frac{\delta(G)}{\delta(P)})=eq of state
but how or why, or is this even correct, please help with these 3 problems, thanks.
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