Question

(b) (i) Starting with the definition of enthalpy, H = U + pl, and using a Maxwell relation, derive the following general equation of state. Write your derivation clearly and logically, showing all steps. You may use the following fundamental equation for change in internal energy without further proof: dU = Tds -pdv.

Answer 1

du = Tds-pdv -70 Dividing by dr keeping Tas constant, we get ) - TC E-POA), - TC29).-p- From Maxwell's relationship, Cesto)= 609)50 (this is First thermodynamic equation of strate) Similarly, H = Tds tvdp 4 OH +V - TT Dividing by dp, keeping Tas Constant, we get (4), = T(*) + VEST Cet T(**)tv -> From Maxbells relationship (O= - -> using © in 0 , we get Scanned with CS CamScanner (this is second themodynamic equation of state)

(li) For an ideal gas PrenRT ->0 V=nRT e pa ng Cente p = ^ Eine From second thermodynamic equation of state , we have use in 3 (9) = v= T(47) > (**, = V-76) (pt) = v-v = V-V ГР.