Question

Under what conditions heat can be given to a substance without raising its temperature

Answer 1

Heat can be given to a substance without raising its temperature,When a substance is changing its physical state[for eg from solid to liquid and liquid to gas ].
The heat energy which has to be supplied to change the state of substance is called its Latent Heat.
Latent heat  does not raise the temperature . But Latent heat must be supplied to  change the state of substance.

Note : The word " Latent" means HEAT is HIDDEN in the substances undergoing the state change.

Answer 2

During a phase change process, heat is absorbed by a substance, without an increase in its temperature. Eg: Boiling of water, where the heat is absorbed as latent heat and does not lead to the increase in the temperature

Hope it answered your question.

Let's move one step further now. Suppose you had asked “Under what conditions heat can be given to a “system” without raising its temperature?”

The answer would have been different:

During any isothermal heat addition process, a system absorbs heat without any change in its temperature.

Cheers !!!!!