Carnot Theorem

Carnot Theren of all engines waiting bhw Constant temp. source and constant the temp sink none has the higher efficiency than Carnot cycle Carnot Cycle T 7= 2 T1 T2 So c P 5=( 2 T1:T3 4 4. T- c 3 3 S3 S2 S1=SA s ve There ave fair processes I'll (i) 1-2 : Isothermal Expansion (ii) 2-3 : Isesthopic Expansis (iii) 3-4 : I sothermsal Compressor 94(4 (iv) 4-1 : Isesthopic compression Taking process 1-2: = P.V. In (VI) W1-2 = RT, In (S) Process 2 - 3: W2-3 = ds i = du + dw dw = - du Pusk 3, dw = - 35 du = CV DT Gy 2/4

W2-3= - - Cv (T3-T2) En c Process 3-4: P3Y3 In (vi) 4 in (" int H3-4 = RT3 In (vg) daily, du 91) Process 4-1: witz APP / W4-1 di° du+dw War W+1=Cr = (T4-II) W=RT,In Total Work (VI) done (T4-T3 and TI=TI) + V3 1 {wester RI3ln ( } (a Now, 2 Taking first do = Law = du+dw (Dividing byT) do=du + dw T ; 3 T T ds= C...TI + PdN T THE do s s pural V's° Cv T (f) +R ln (NF) It is zew. Esthopy O= - even (IF) + Rln (=) du of a In (If) T3 R ln (VL) V3

Similarly, (i) v) a in( ii) ( V4 Rln Vi Since a In ( T2 13 ) = cv)ln ( THE Ty TI ) Ken (V2 ) = p/ln ( van) Assuming V2 the ratus are same ( Cancel dericas in) V3 V4 Electronic ad count V2 VI wt Milner V2 ie; V3 = 2 its V4 VI ( - 1/2 1 . W= RT, ln (vi) - RT3 ln (VA) substituting 2 in W ) W.D Now difficulty H.supplicel RT.CH RT3 In (iii) N RTI ln (V2/ V2 ) n R ln N V/2, ( T1-T3) V2 R ln x T1 V! T3= T4 T1-T3 mg n = / 11- - T4 n 12 v/- Tu (Some) = TV T1 (sink)