The temperature of $5$ moles of a gas at constant volume is changed from $100^{\circ} C$ to $120^{\circ} C$. The change in internal energy is $80 \,J$. The total heat capacity of the gas at constant volume in $J/K$ is:

The figure below shows the variation of specific heat capacity $(C)$ of a solid as a function of temperature $(T)$. The temperature is increased continuously from $0$ to $500 \ K$ at a constant rate. Ignoring any volume change,which of the following statement$(s)$ is (are) correct to a reasonable approximation?
$(A)$ The rate at which heat is absorbed in the range $0-100 \ K$ varies linearly with temperature $T$.
$(B)$ Heat absorbed in increasing the temperature from $0-100 \ K$ is less than the heat required for increasing the temperature from $400-500 \ K$.
$(C)$ There is no change in the rate of heat absorption in the range $400-500 \ K$.
$(D)$ The rate of heat absorption increases in the range $200-300 \ K$.

Define molar specific heat and state its $SI$ unit.

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 $kJ$)

The quantities of heat required to raise the temperature of two solid copper spheres of radii $r_{1}$ and $r_{2}$ $(r_{1} = 1.5 r_{2})$ through $1 \ K$ are in the ratio:

Is the specific heat of water greater than that of sand?