Tesla embraces the heat engine

Tesla decides to go back to basics with their new line, the Entropica series. Leaving aside their rather successful venture into electric engines, Tesla pivots to embrace the heat engine, which uses two heat blocks of initial temperature T+T_+, and TT_- to drive an engine through a thermodynamic cycle (pictured above).

Concretely, each cycle drives some heat δQ\delta Q from the hot reservoir to the cold reservoir, and the engine performs some work δW\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+T_+, and raises the temperature TT_-, until T+=T=TT_+=T_-=T^*, at which point the engine can do no further work.

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

Assumptions and Details

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

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