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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 [tex]-P = (\frac{(\delta(F))}{(\delta(V))})_T[/tex], and thus all i have to do is differentiate the negative of the above function for F with respect to V, and the [tex]J(T)[/tex] function disappears.

3. The Gibbs function of a certain gas is:

Now, the answer in the book is:

a).[tex]f = c_v(T-T_0)-c_vT\ln(T/T_0)-RT\ln(v/v_0)-s_0T[/tex]

b).[tex]g = c_p(T-T_0)-c_pT\ln(T/T_0)+RT\ln(P/P_0)-S_0T[/tex]

totally lost here, where do i begin?b).[tex]g = c_p(T-T_0)-c_pT\ln(T/T_0)+RT\ln(P/P_0)-S_0T[/tex]

2. The Helmholtz function of a certain gas is:

[tex]F = -\frac{n^2a}{V} - nRT \ln(V-nb) + J(T)[/tex],

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 [tex]-P = (\frac{(\delta(F))}{(\delta(V))})_T[/tex], and thus all i have to do is differentiate the negative of the above function for F with respect to V, and the [tex]J(T)[/tex] function disappears.

3. The Gibbs function of a certain gas is:

[tex]G = nRT\ln(P) + A + BP + \frac{CP^2}{2} + \frac{DP^3}{3}[/tex](

where A,B,C, and D are constants. Find the equation of state of the gas.Now, the answer in the book is:

[tex]nRT + BP + CP^2 + DP^3[/tex]

the only way i see to get this is to differentiate the expression for with respect to P, giving:[tex]\frac{nRT}{P} + B + CP + DP^2[/tex]

and then multiplying this result through by P, or in other words, the equation of state is given by:[tex]P(\frac{\delta(G)}{\delta(P)})=eq of state[/tex]

but how or why, or is this even correct, please help with these 3 problems, thanks. :surprised
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