On what does the heat required to increase the temperature of a substance depend?

Write the old and new definition of calorie.

At temperatures close to $0\ K$, the heat capacity $C$ of a certain solid is related to its temperature $T$ by the equation $C = aT^3$, where $a$ is a constant characteristic of the solid. Heat is supplied to the solid at a steady rate. Which graph best represents the variation of its temperature $T$ with time $t$?

If the specific heat of a substance is infinite,it means that:

How much heat energy is gained when $5\, kg$ of water at $20^{\circ}C$ is brought to its boiling point? (Specific heat of water $= 4.2\, kJ\, kg^{-1} {^{\circ}C}^{-1}$)

What is the value of the specific heat of all substances at absolute zero temperature?