On what does the value of heat capacity depend?

The specific heat of a substance at temperature $T^{\circ}C$ is given by $C = \alpha T^2 + \beta T + \gamma$. The amount of heat required to raise the temperature of a mass $m \, g$ of the substance from $0^{\circ}C$ to $T_o^{\circ}C$ is .......

Two spheres made of the same substance have diameters in the ratio $1:2$. Their thermal capacities are in the ratio of:

$A$ heater supplying constant power $P$ watts is switched $ON$ at time $t=0$ to raise the temperature of a liquid kept in a calorimeter of negligible heat capacity. $A$ student records the temperature of the liquid $T(t)$ at equal time intervals. $A$ graph is plotted with $T(t)$ on the $Y$-axis versus $t$ on the $X$-axis. Assume that there is no heat loss to the surroundings during heating. Then,

The thermal capacity of $100 \,g$ of aluminum (specific heat $= 0.2 \,cal / g ^{\circ} C$) is ............ $cal / ^{\circ} C$.

Why is water used as a coolant?