Question

1(a) Show that the entropy of the van der Waals gas is ơ-N{InP0(NNb1 Show that the energy is U 3Nt/2 - N2a/V. (c) Show that the enthalpy H U pV is 5/2). (b) the results are given to first order in the van der Waals correction terms a and b.

Answer 1

(i) sigma = N [log (v - N_b s/N] + 5/2 (where sigma = Entropy] (ii) v = 3/L NL - N^Y a/v (v = Energy] (iii) H = U + pv (h = Enthalpy) H (z, v) = 5/2 + n^2 bz/v - 2 n^2 a/v H(z, p) = 5/3 N_2 + Nbp - 2 Nap/z ok, let's start with vander warls Gas First we know vander wals Gas equation is (p + av^2/r^2) (-r - ND) = NRT when av^2/v^2, nb are correction term that v want observed, which account for charge of gas from ideals behaviour the ans why gas decided from ideal behavior To get Entropy sigma, we ve to derivate w.r.t T (v = cons) sigma = -(Partialdifferential A/Partialdifferential T)_v To get Internal Energy U we need help Equation v = A + T sigma Now A ideal gas is c non-intracting particles It has Equation pv = Nk_BT = N_T