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# Can the temperature of a system remain constant even though heat flows into or out it? If so, give examples.

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Yes, it is possible that the temperature of a system (change in temperature is proportional to internal energy $\Delta U$) remain constant even though heat ($Q$) flows into or out of it. In the case, the total heat supplied to the system ($Q$) is changed into work done ($W$) without increasing its temperature (the internal energy of the system).

It is an application of thermodynamics first law with equal amount of work done on or by the system:

$\Delta U = Q + W = 0$

$Q=W$ and internal energy (temperature) of the system is remains same.

Isothermal process is one of the examples for the given situation, while substances take phase changing, its temperature remains constant though heat transition takes place, for example, the water will remain at 0$\text{\textdegree}$C even though heat is being put into the system until all the ice melts.

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