$A$ source supplies heat to a system at the rate of $1000 \, W$. If the system performs work at a rate of $200 \, W$,the rate at which the internal energy of the system increases is $....... \, W$.

$A$ system is given $300$ calories of heat and it does $600$ joules of work. How much does the internal energy of the system change in this process? $(J = 4.18 \text{ Joules/cal})$ (in joule)

$A$ gas is expanded from an initial state to a final state along a path that consists of $(a)$ an isothermal expansion doing $40 \,J$ work,$(b)$ an adiabatic expansion doing $W$ work,$(c)$ an isothermal expansion doing $30 \,J$ work. If the total change in the internal energy of the gas is $-20 \,J$,the work done by the gas during the adiabatic expansion $W=$ (in $\,J$)

During the process $A \rightarrow B \rightarrow C$,the work done is $50 \, J$ and the heat supplied is $20 \, cal$. Find the change in internal energy between $A$ and $C$ in $J$. (in $, J$)

$Assertion:$ 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.

If $\Delta Q$ and $\Delta W$ represent the heat supplied to the system and the work done on the system respectively,then the first law of thermodynamics can be written as,where $\Delta U$ is the change in internal energy.