Can change in energy take place in a system when there is no change in temperature?

Dear Student,

No, change in energy will not take place if there is no change in temperature. 
Internal energy is a function of temperature. This is because internal energy is the sum of kinetic and potential energies of the particle that form the system and according to kinetic molecular theory, temperature of a gas is directly proportional to the average kinetic energy of its particle. So, we can say that internal energy is directly proportional to temperature.
Therefore, if ΔT=0 then ​ΔU=0.

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