Question

2.) As in problem 1, show that a. dH = Tds + VdP b. Aš = C, In - Rin for an ideal gas 3.) Ethene may be regarded as an ideal gas and its heat capac regarded as an ideal gas and its heat capacity is temperature dependent according to 7 (T) = 16.4104R-008. a. Confirm that 38.75 J K is the value for the entropy change of heating one mol of ethane from 300 to 600K at constant volume. b. Recall that Co-CunR. Confirm the value of 44.50 JK when heating at constant pressure. C. Also confirm the answers from a) and b) using AS, = AS + R In 2. First, prove this equation is valid and then use it to check if your numerical answers to a) and b) differ by R In(600/300) = R-In(2)

Answer 1

79) 106 have to show that dH= Tas+vdp According to first law of thermodynamics ; be know that I du= det do e n 40 Now, From second law of thermodynamics; we go dszda E 2 For an reversible system; ds=de = (de = Tds] And . na for reversible System work done elw = - Pav albo absays. putting these value in egh ; we get dU = Tds-pav] tegn Now, we know that 1. H= U+ PV differenziale Both Side, we get dH= dut d CPV)

- dll do 4 Pdv Avd Pa Putting value of du from em e, we get - du = Tds-pavit sau tulp = falu = Tds t velp Hence prove. b) we have to show that; | Ds = cp in 12 - Rln P 22 | e Form above part we know that of cil = Tds + vap 7 e • And on from very fundamental ) we know change in Enthalky lie. S dr= cp dT 1 - 9 from egno & en ; we get e Tds + vdp = epdt Tds = cp dT _vdp ds = cp d I vdp 100

Now According to ideal gas low for a mele - [PURT] ng na paran Pieting these value in ej" 3); weger Les = cpd I _ R de Insigrate Both Side '; we get 111111111111111111 T 1 Barth Cp SR is const. so we get - ps = cplint - RM per Hence prove