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Derive the expression for Carnot engine efficiency.

Answer» <html><body><p></p>Solution :Efficiency of a Carnotenginr: Efficiency is <a href="https://interviewquestions.tuteehub.com/tag/defined-947013" style="font-weight:bold;" target="_blank" title="Click to know more about DEFINED">DEFINED</a> as the ratio of <a href="https://interviewquestions.tuteehub.com/tag/work-20377" style="font-weight:bold;" target="_blank" title="Click to know more about WORK">WORK</a> done by the working substance in one cycle to the amount of heat extrcted from the source. <br/> `eta=("work done" )/("heat extracted")=(W)/(Q_(H))` <br/> From the <a href="https://interviewquestions.tuteehub.com/tag/first-461760" style="font-weight:bold;" target="_blank" title="Click to know more about FIRST">FIRST</a> law of thermodynamics, `W=Q_(h)-Q_(L)` <br/> `eta=(Q_(H)-Q_(L))/(Q_(H))=(Q_(L))/(Q_(H))` <br/> Applying isothermal conditions, we <a href="https://interviewquestions.tuteehub.com/tag/get-11812" style="font-weight:bold;" target="_blank" title="Click to know more about GET">GET</a> <br/> `Q_(H)=muRT_(H) In((V_(2))/(V_(1)))` <br/> `Q_(L)=muRT_(L) In((V_(3))/(V_(4)))` <br/> `therefore (T_(L))/(T_(H))=(Q_(L) In(V_(3))/(V_(4)))/(Q_(H)In(V_(2))/(V_(1)))` <br/> By applying adiabatic conditions we get , <br/> `T_(H)V_(2)^(y-1) = T_(L) V_(3)^(y-1)`<br/> `T_(H)V_(1)^(y-1) = T_(L) V_(4)^(y-1)` <br/> By dividing the above two equations we get, <br/> `(V_(2)/(V_(1)))^(y-1)=(V_(3)/(V_(4)))^(y-1)` <br/> Subsitituting <a href="https://interviewquestions.tuteehub.com/tag/equation-974081" style="font-weight:bold;" target="_blank" title="Click to know more about EQUATION">EQUATION</a> (5) in (4), we get <br/> `(Q_(L))/(Q_(H)) =(T_(L))/(T_(H))` <br/> `therefore` The effiency `mu=1-(T_(L))/(T_(H))`</body></html>


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