An electric heater supplies heat to a system at a rate of $100\;W.$ If the system performs work at a rate of $75\;J/s,$ at what rate (in $J/s$) is the internal energy increasing?

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 ............ $J kg^{-1}$.

$A$ thermally insulated rigid container of $1 \,L$ volume contains a diatomic ideal gas at room temperature. $A$ small paddle installed inside the container is rotated from the outside,such that the pressure rises by $10^{5} \,Pa$. The change in internal energy is close to ............... $J$.

Which of the following laws of thermodynamics defines the term internal energy?

Three moles of a gas at a temperature $T$ is heated to thrice its volume by keeping the pressure constant. If $\gamma$ is the ratio of specific heats,then the increase in internal energy of the gas is

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: