Negative heat capacity and thermal reservoir

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Afonso Campos
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Say you have an object with a negative heat capacity. This means that the object increases in temperature as it radiates energy and decreases in temperature as it absorbs energy.

I don't understand why this object cannot be in thermal equilbrium with a reservoir.

Any help would be greatly appreciated.
 
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If it is contact with something with positive energy, the negative temperature system will transfer energy to the positive temperature system. The entropy always increases as long as the sign of the temperature is different - but thermal equilibrium is the state of maximal entropy.
 
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Thank you. I understand it now.