$4200\, J$ of work is required for:

$A$ current-carrying wire heats a metal rod. The wire provides a constant power $(P)$ to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature $(T)$ in the metal rod changes with time $(t)$ as:
$T(t) = T_0(1 + \beta t^{1/4})$
where $\beta$ is a constant with appropriate dimensions,while $T_0$ is a constant with the dimension of temperature. The heat capacity of the metal is:

What is the heat capacity of copper of $40 \, g$ and specific heat $0.3 \, erg \, g^{-1} (^{\circ} C)^{-1}$?

$A$ small electric heater is used to heat $200 \,g$ of water. The time required to bring all this water from $40^{\circ} C$ to $100^{\circ} C$ is $200 \,s$. If the specific heat of the water is $4200 \,J \,kg^{-1} \,K^{-1}$, then the power supplied by the heater is: (in $\,W$)

The temperature of $5$ moles of a gas which was held at constant volume was changed from $100^{\circ}C$ to $120^{\circ}C$. The change in internal energy was found to be $80$ Joules. The total heat capacity of the gas at constant volume will be equal to ...... $J/K$.

Write the old and new definition of calorie.