I am brushing up on my thermodynamics knowledge at the minute and am wondering if there is a process or circumstance in which a body receives heat but the temperature of the body decreases?
In an isothermal process, a body can receive heat and the thermal equilibrium of the system is still maintained. Is there are example of a body receiving heat and the temperature of the body decreasing?
There's plenty of examples of doing this through chemical means. I have an ice pack which, when a divider is broken and the components mixed, begins to continuously cool itself via a chemical reaction. This is true, even as the pack receives heat.
This implies a negative heat capacity. Stars have this property, although in their case it's more "releases heat but the temperature increases". Perhaps the least luminous of two close stars in a binary system would receive net heat.
The first law of thermodynamics is $$\Delta U = Q - W$$
$U$ is the total internal energy and is proportional to temperature. If $Q$ (heat supplied) is small, but a gas expands and does work $W$, then the temperature can decrease.
An example of this is an aerosol spray can at room temperature - when we hold it, it begins receiving heat from our hand. Then when we press the button it releases the deodorant, for example, (you may have noticed that the spray feels cold). The gas expands, does work of $W= P\Delta V$ (where $P$ is pressure and $\Delta V$ is the change in volume) and cools down.
If you could arrange an experiment so that the aerosol can sprayed into an enclosed box, the final temperature of the can/box system would have decreased, even though heat was added.
