Carnot cycle with efficiency > 1

[paweld]

Is it possible (at least theoretically) to construct engine which uses Carnot cycle
and two reservoirs with temperatures $$T_1<0<T_2$$ (one of them has
negative temperature which is possible e.g. in case of two-state paramagnet).
Such cycle would have efficiency greater then 1.

(of course the reservoir with negative temperature is "hotter")

 

[Andy Resnick]

No. Please see earlier threads.

 

[russ_watters]

Is it possible (at least theoretically) to construct engine which uses Carnot cycle
and two reservoirs with temperatures $$T_1<0<T_2$$ (one of them has
negative temperature which is possible e.g. in case of two-state paramagnet).
Such cycle would have efficiency greater then 1.

(of course the reservoir with negative temperature is "hotter")

I'm not following - you want the cold reservoir to be hot and the hot reservoir to be cold? If you plug that into the efficiency equation, you get an efficiency below zero! In other words, nothing.

And a temperature below zero...you mean below absolute zero?

http://en.wikipedia.org/wiki/Carnot_cycle

 

[Pythagorean]

Is it possible (at least theoretically) to construct engine which uses Carnot cycle
and two reservoirs with temperatures $$T_1<0<T_2$$ (one of them has
negative temperature which is possible e.g. in case of two-state paramagnet).
Such cycle would have efficiency greater then 1.

(of course the reservoir with negative temperature is "hotter")

Temperature conventions that use negative values do not do so for any absolute physical reasons. They are more designed around human convenience (water's state changes for Celsius and I think human comfort for Farenheit).

That is why we have the Kelvin scale. You can't go below 0 Kelvin because the Kelvin temperature relates directly to energy, which can't be negative. Kelvin best represents the actual thermodynamics, which doesn't allow for a negative number.

 

[xxChrisxx]

Sounds like meaningless twaddle to me.

 

[jack action]

Is it possible (at least theoretically) to construct engine which uses Carnot cycle
and two reservoirs with temperatures $$T_1<0<T_2$$ (one of them has
negative temperature which is possible e.g. in case of two-state paramagnet).
Such cycle would have efficiency greater then 1.

(of course the reservoir with negative temperature is "hotter")

No. The reason is that negative temperatures, although numerically lower than zero, are higher than infinite temperature. From http://en.wikipedia.org/wiki/Negative_temperature#Heat_and_molecular_energy_distribution":

"The temperature scale from cold to hot runs:

+0 K, . . . , +300 K, . . . , +∞ K, −∞ K, . . . , −300 K, . . . , −0 K."

On the "other side", everything works in reverse: when you add energy, the temperature decreases; when you remove energy, the temperature increases. So let's assume you have a T_hot that is negative and a T_cold that is positive. Going from T_hot to −∞ K, you will need to add energy. Then going from +∞ K to some temperature T_x you will recover the amount of energy you spent "cooling" your negative temperature, making your net energy balance = 0. Finally going from T_x to T_cold will represent the actual energy you will recover. So the actual Carnot cycle have to be calculated with T_x as the hotter temperature.

Not a pro on the subject, that is just my understanding.