- #1

nonequilibrium

- 1,439

- 2

For a reversible heat engine between temperatures [tex]T_1[/tex] and [tex]T_2[/tex], the ratio of heat going in and out the engine is [tex]\frac{Q_1}{Q_2} = \frac{T_1}{T_2}[/tex] (second law).

Say [tex]T_1 = 200 K[/tex] and [tex]T_2 = 273 K[/tex], then heat goes from 2 to 1 and as we can see, the ratio of heat that goes in the engine is indeed bigger than what comes out ( = logical, due to delivery of work).

Take two ideal paramagnets, each at a negative temperature (note: negative temperature > positive temperature; the scale goes [tex]0 \to \infty \to - \infty \to 0[/tex]).

Now say [tex]T_1 = -200 K[/tex] and [tex]T_2 = -273 K[/tex], then heat will go from 1 to 2 (Because the entropy of paramagnetic reservoir 1 will raise more than the drop in that of paramagnetic reservoir 2). The ratio of heat going in and out hasn't changed due to the minus cancelling in top and bottom. This says that the heat going in from 1 into the engine is less than the heat deposited from the engine into 2.

What's the explanation?