Question

Need help with problem 6

5. Consider the general Carnot cycle discussed in Lecture #9, in which we take a mole of ideal gas through a cyclic path of thermodynamic states and processes involving successive isothermal and adiabatic expansions and compressions. (a) Evaluate the work terms Wab and wcd for the isothermal steps, in terms of: the initial and final volumes involved; and the temperatures involved. (b) Do the same for the adiabatic steps, i.e., calculate Wbc and wda. (c) Show how the overall work performed, Wcycle, can be written in terms of the two temperatures involved. (d) Evaluate the efficiency cycle of the overall process, and show that it is necessarily less than 1. qab 6. Carry out a Carnot cycle like the general one in problem 5 above, and calculate the efficiency associated with it, after choosing a pair of operating temperatures, and initial and intermediate volumes. What about if other intermediate volumes were involved?

Answer 1

Ти > Тc. ЛВ 3 ср цаl орума ADA B C adiabatic for I sottunal brous. W = RT en Vf as Pov PRT/ - Voni WAB = RTG en (VB/A) O O = OU- RAB- WAB. for wed= RTc en (vol for Adiabatic process. no=00=960- q woo Lor=o W = P R Timi 10. 19 : Y-1 V -RT as av w- Time projet Puy = , const. ). Y-1

W -R Time PV = K, const. Y- abco = qd adiabatic. We = RTn (Vol / il 7 tv Wda = RTC (Vd) Statef? Y- val -) for acycle it is o acych - wagels. Черевет со шерла - 6 - Weyel WAB TWD RT en (VB/VA) + RT ln ( Jove)

Weych, QARTOLD , QAB QAR 1 aCD YAB - (4) (5) sushat how UAV connected PAVA - PV Const. tup? - PAXPp = VB x NC PVC = POD Pc P o vp. PAVY = P vo for AD Proussadiabatis process) PBVBY = Povo By Ideal Gaslaw PAVA = RT & P = RTC & VB PB = R T & V C at B M 6 с. ERT Ad E at a at D

PA XPD - Pc PB балал 4 че те и V Valve S v = vc - O for 4 - Warch = 1- RTC en (Volver qAB Now To is for cold temp. & Infor hot fluid i son n =1-Tc Tn (n<1

If I assume Th=600k f Te =300k. n = 1-300 =0.5 600 No Paint of choosing volume as y cambi calculated romeon & I e In=1- Tc
When a cycle is completed a state function like internal energy will be o .

Wcycle has been representd In Temperature

Also efficiency is proved to be less than 1

And since efficiency dosnt involve any volume term only Temperature is sufficient so I believe is no point calculating intermediate volume whatsoever only temperature suffices

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