$1 \text{ cm}^3$ of water at its boiling point absorbs $540 \text{ calories}$ of heat to become steam with a volume of $1671 \text{ cm}^3$. If the atmospheric pressure = $1.013 \times 10^5 \text{ N/m}^2$ and the mechanical equivalent of heat = $4.19 \text{ J/calorie}$, the energy spent in this process in overcoming intermolecular forces is ..... $\text{cal}$. (in $\text{cal}$)

$Assertion:$ The heat supplied to a system is always equal to the increase in its internal energy.
$Reason:$ When a system changes from one thermal equilibrium to another,some heat is absorbed by it.

$A$ resistance coil connected to an external battery is placed inside an adiabatic cylinder fitted with a frictionless piston and containing an ideal gas. $A$ current $i$ flows through the coil which has a resistance $R$. At what speed must the piston move upward in order that the temperature of the gas remains unchanged? Neglect atmospheric pressure.

The first law of thermodynamics states that:

When $150 \ J$ of heat is supplied to a system,the work done by the system is $110 \ J$. The change in the internal energy of the system is ....... $J$.

Consider $1 \,kg$ of liquid water undergoing a change in phase to water vapour at $100^{\circ} C$. At $100^{\circ} C$,the vapour pressure is $1.01 \times 10^5 \,N m^{-2}$ and the latent heat of vaporization is $22.6 \times 10^5 \,J kg^{-1}$. The density of liquid water is $10^3 \,kg m^{-3}$ and that of vapour is $\frac{1}{1.8} \,kg m^{-3}$. The change in internal energy in this phase change is nearly ............ $J kg^{-1}$.