$A$ system is taken from state $A$ to state $B$ along two different paths. The heat absorbed and work done by the system along these two paths are $Q_1, Q_2$ and $W_1, W_2$ respectively,then

$1\,kg$ of water at $100^{\circ}C$ is converted into steam at $100^{\circ}C$ by boiling at atmospheric pressure. The volume of water changes from $1.00 \times 10^{-3}\,m^3$ as a liquid to $1.671\,m^3$ as steam. The change in internal energy of the system during the process will be $........kJ$ (Given latent heat of vaporisation $= 2257\,kJ/kg$. Atmospheric pressure $= 1 \times 10^5\,Pa$)

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

Given below are two statements. One is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$ : If $dQ$ and $dW$ represent the heat supplied to the system and the work done on the system respectively,then according to the first law of thermodynamics $dQ = dU - dW$.
Reason $R$ : The first law of thermodynamics is based on the law of conservation of energy.
In the light of the above statements,choose the correct answer from the options given below:

$A$ monoatomic gas of $n$ moles is heated from temperature $T_1$ to $T_2$ under two different conditions: $(i)$ at constant volume and $(ii)$ at constant pressure. The change in internal energy of the gas is

In a thermodynamic process,the pressure of a fixed mass of a gas is changed in such a manner that the gas releases $30 \ J$ of heat and $10 \ J$ of work is done on the gas. If the initial internal energy of the gas was $30 \ J$,then the final internal energy will be ........ $J$.