Carnot engine acting upon another Carnot engine

[bjnartowt]

Homework Statement

Suppose an amount of power P_{\ell} is delivered to a load by a black box with potential difference V_T across it, driving current I through a single loop. If an amount of power P_b is applied to the black box, to sustain I at V_T, then the efficiency of this black box acting as an engine is P_{\ell}/P_b.

Now, suppose you have exactly the same black box, exactly the same load, but an additional device (in series, so it's still a single loop) applying an emf E_{ap} and a current I. The black box may still supply power, but if E_{ap} is large enough in magnitude, the black box becomes a load. However, the black box dissipates less power when the amount of power P_b applied earlier is applied to the black box. More power P_{\ell} is delivered to the load due to the application of P_b.

My question is: what would be the efficiency of the black box (if such a quantity exists) in its increasing P_{\ell} due to the application of P_b when it is "assisting" the applied emf E_{ap}?

Homework Equations

Energy conservation is P_{\ell} = V_T * I in the "non-assisted" case, and P_{\ell} = (E_{ap} - V_T) * I in the "assisted" case.

The Attempt at a Solution

I tried "guessing" an efficiency of P_{\ell} / (P_b + I * E_{ap}). If P_b is the heat flow from a temperature-difference between temperatures T_L and T_R, I ought to get something bounded between 0 and the Carnot efficiency.

 

[Andrew Mason]

Are you able to explain how this problem relates to thermodynamics? Where does this problem come from?

AM