The specific heat of a substance varies with temperature as $c = 0.20 + 0.14t + 0.023t^2 \, (cal/g \cdot ^\circ C)$. The amount of heat required to raise the temperature of $2 \, g$ of the substance from $5 \, ^\circ C$ to $15 \, ^\circ C$ is: (in $, cal$)

Water of mass $5 \ kg$ in a closed vessel is at a temperature of $20^{\circ} C$. If the temperature of the water when heated for a time of $10 \ minutes$ becomes $30^{\circ} C$, then the increase in the internal energy of the water is (Specific heat capacity of water $= 4200 \ J \ kg^{-1} \ K^{-1}$) (in $kJ$)

$A$ lead bullet of mass $10 \ g$ travelling at $300 \ m/s$ strikes against a block of wood and comes to rest. Assuming $50\%$ of heat is absorbed by the bullet, the increase in its temperature is (Specific heat of lead $= 150 \ J/kg \cdot ^{\circ}C$) (in $^{\circ}C$)

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

On what does the value of heat capacity depend?

Derive the equation for the molar specific heat capacity of solids.