Show that, for a Carnot engine operating between reservoirs at temperatures T1 and T2 (T1 >...

Show that, for a Carnot engine operating between reservoirs at temperatures T1 and T2 (T1 > T2), the thermal efficiency is given by

Eta sub R = T1-T2/T1

Solutions

Expert Solution

The Carnot engine cycle is represented by the diagram below.

The Carnot engine has two thermal reservoirs -- one at high temperature T₁ and the other at low temperature T₂. The engine consists of a reversible isothermal expansion from state 1 to 2, reversible adiabatic expansion from state 2 to 3, a reversible isothermal compression from state 3 to 4 and lastly a reversible adiabatic compression to state 1.

During processes 2-3 and 4-1, there is no heat interaction as they are adiabatic. Heat exchange in process 1-2 is

Heat exchange in process 3-4 is

Net heat interaction = Net work done

W =

The processes 2-3 and 4-1 are reversible, adiabatic and hence

V₂/V₃ = V₁/V₄ or V₂/V₁ = V₃/V₄

Then efficiency = Work done / heat input =

genius_generous answered 1 year ago

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