carnot theoremno heat engine operating in cycle

Question

Carnot Theorem:

No heat engine operating in cycle between the two given thermal reservoir, having fixed temperature can be more efficient than reversible engine operating between same thermal reservoir.

* Thermal efficiency  η th  = Work out/Heat supplied

* Thermal efficiency of a reversible engine (  ηrev)

η_rev= (T₁  - T₂)/T₁  ;

* No engine can be much efficient than reversible carnot engine that is η_rev > η_th

Carnot Efficiency

= (Heat added - Heat rejected) / Heat added = [mRT₂lnV₂/V₁ - mRT4lnV₃/V₄]/ mRT₂lnV₂/V₁

= 1- T₁/T₂