Question

Section IV 1 (av vap 1 and isothermal compressibility KT use the 1. Knowing expansion coefficient a T Maxwell relations to justify the following equations: (a) The Joule coefficient is Ay Justify t,Cy p-aT/Kr. T (b) Justify the thermodynamic equation of state tr -p. av ан Justify Hr=-T T +V (c) The isothermal Joule-Thomson coefficient is ur

Answer 1

Section - LV : i bu. y Expansion coefficient, a = Corp Sother mal compressiblwing, Kr= - + (0) Maxwell relations ; C (3u o Po let) p = -2 b) Thermodynamic equation of state: A+ = + (2P-P Justification : We have the basic thermodynamic equation → du = Tas - Pav Dividing by du at constant I, we have a leo ya Tan-P Using Max wel relcultonship > 206) 7 = This B Thermodynamic equation of state.

ay Joule coefficient, Mj = @). uj Cu = p - online Justification : - We know, cu = (ou du Now, Mj Cu = key could Firm eyelic rule, ceny, ()Case) = -1 Mi 6 = 3 --( Now, (uz C = -(-- O From Cyclit rule, rey, BC F C = -1 lavarle - V - - = @Ye} Multiplying the numerator q denominator on RM-3 by VP & we obtain a lavarle Centro - (Var) = a la and Ⓡ. we get → Using equation 0, Now, Ūy ev = -lauja My Cu = P-Ta AT

<> Isothermal Joule Thomson coefficient, ly = 2 Justificalim : We have the basic Thermodynamic equation → dH = Tas + udp dividing by dp Kleeping T constant, we have DE = T (2)tu Fron muawel relations (03- Bebe Now (eh) = -t en de tu
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