Tesla embraces the heat engine

Concretely, each cycle drives some heat \(\delta Q\) from the hot reservoir to the cold reservoir, and the engine performs some work \(\delta W\) to propel the car, such that the engine returns to its original state after each cycle. Clearly, each cycle lowers the temperature \(T_+\), and raises the temperature \(T_-\), until \(T_+=T_-=T^*\), at which point the engine can do no further work.

Find \(T^*\) (in deg Kelvin) at the point where the engine stops running.

Assumptions and Details

• The entire process is thermodynamically reversible.
• \(T_+\) = 423\(^\circ\) K
• \(T_-\) = 300\(^\circ\) K
• Both heat reservoirs are metal blocks of heat capacity \(\gamma\)