$1\,kg$ 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 $= 1 \times 10^5\,Pa$)

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:

Which of the following statements is incorrect regarding the first law of thermodynamics?

The internal energy of an ideal gas is given by $U = 1.5 PV$. It expands from $10 \ cm^3$ to $20 \ cm^3$ against a constant pressure of $2 \times 10^5 \ Pa$. Heat absorbed by the gas in the process is (in $J$)

If heat given to a system is $6 \, kcal$ and work done is $6 \, kJ$,then the change in internal energy is ....... $kJ$.

$A$ 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.