In supplying $400$ calories of heat to a system,the work done will be

$1.00 \ kg$ of liquid water at $100^{\circ} C$ undergoes a phase change into steam at $100^{\circ} C$ at $1.0 \ atm$ (take it to be $1.00 \times 10^5 \ Pa$). The initial volume of the liquid water was $1.00 \times 10^{-3} \ m^3$ which is changed to $2.001 \ m^3$ of steam. Find the change in the internal energy of the system. [Use heat of vaporization $\simeq 2000 \ kJ \ kg^{-1}$] (in $kJ$)

The first law of thermodynamics is concerned with the conservation of

$Assertion:$ 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.

$1 \, kg$ of a gas does $20 \, kJ$ of work and receives $16 \, kJ$ of heat when it is expanded between two states. $A$ second kind of expansion can be found between the initial and final states which requires a heat input of $9 \, kJ$. The work done by the gas in the second expansion is ....... $kJ$.

When the amount of work done is $333 \ cal$ and the change in internal energy is $167 \ cal$,then the heat supplied is ....... $cal$.