Carnot engine in a room with heat loss to equilibrium

[Lh0907]

Homework Statement

The room has temperature T,and outside of temperature is T0. Due to Carnot engine located in the room, this engine makes to give quantity of heat(Power P) outside -> inside.

And the room loses heat which ratio is a(T-T0).(a is just constant.)

What's the equilibrium temperature?

(This problem is not complete. I couldn't memorize totally this problem.

But outline of this problem maybe correct.)

Homework Equations

I think Entropy of Carnot engine(ds).

(This problem is not on the book.

It's only a problem which I saw at once.)

The Attempt at a Solution

I try to get solution through Entropy of Carnot engine maybe related with this problem.

But I'm not sure I'm wrong or correct.

Homework Statement

Homework Equations

The Attempt at a Solution

 

[member 553083]

The equilibrium temperature is given by the Carnot engine working between two temperatures, T and T0. The Carnot engine absorbs a certain amount of heat energy (P) from T0 and releases the same amount of heat energy to the room at temperature T. The balance between the heat absorbed from T0 and the heat released to the room is given by the equation: P = a(T - T0) where a is a constant. The equilibrium temperature is then given by the equation: T = T0 + P/a This equation gives the temperature of the room when the heat energy absorbed and released by the Carnot engine are in balance.