Question

is heat supplied to a system always equal to the increase in its internal energy ​

Answer 1

Hii here your answee

The internal energy is equal to the heat of the system. The surrounding heat increases, so the heat of the system decreases because heat is not created nor destroyed. Therefore, heat is taken away from the system making it exothermic and negative.

Hope it will help you

Answer 2

Heat supplied to the system is equal to the change in internal energy only at constant volume