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Car not's Theorem, It states,, No engine is oferating betwe en, two given temperatures can be more, Than a Carnot engine (r.e. a reversible enging), efficient, bperating between Hhe same temperatures.", Proof Let us consider two heat engines I and,, R, bet ween the saurce at temperature, warking, TiK and sink at Femperature T,k. Let engine, I be irreversible and engine R, engine, be reversikle (carnot) engine-, Suppose that the quanitity of warking subslana, iu ether engine is adjusted in such a, manner that 4he work ferfermed per cycle is, Same iu each Case -, Let the energy changes for ene cycle., Engine R, are -., Engine I, 1. Heat absoobed at Tq, 2. work performed, 3. Heat rejected at Tz, Qg = Qy-W, N7 = W, Then effiueny of engine I,, and efficiency df engine R,, NR -

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Suppose, the irreversible engine 7 is, more efficuent than the reverbible, engine R, theu, Source T, R, Sink Tz, Qq, or, Q; 7Qd, Thus (Q-21) is a, fobitive quantily ., Now let the two engines be coupled together mu, Such a way that as the engine I works directly it, drives the engine R in reverse direction as shown, iu the figure · Now R works as refrigerator driven, by I., Thus R will Q-w) heat frem the sink at, temp. Tz K, wark w has been ferTo ferformed on, 2t and it rejects heat Q to source at Femp., The required work W to be done on R is, supplie d by I di'redly, intlis uay engine I, and Refrigeralo R coupled tegether formsca, Belf acting device]