Question
Should the internal energy of a system necessarily increase if its temperature is increased?

Answer

Internal energy of a system increases if its temperature increases. This is valid only for the system of ideal gases and not for all the systems. For example: During meting process, temperature of the system remains constant, but internal energy change increases by mL.$\Rightarrow\Delta\text{U}=\text{mL}$
Here, m = Mass of the solid L = Latent heat of the solid

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