If $Q$,$E$,and $W$ denote respectively the heat added,change in internal energy,and the work done by a closed cycle process,then

In a thermodynamic process,$200 \ J$ of heat is given to a gas and $100 \ J$ of work is also done on it. The change in internal energy of the gas is ........ $J$.

$A$ gas is at a constant pressure of $4 \times 10^5 \,N/m^2$. When a heat energy of $2000 \,J$ is supplied to the gas, its volume changes by $3 \times 10^{-3} \,m^3$. What is the increase in its internal energy (in $\,J$)?

Heat given to a system is $35 \ J$ and work done by the system is $15 \ J$. The change in the internal energy of the system will be ..... $J$.

The $P-V$ diagram of a system undergoing a thermodynamic transformation is shown in the figure. The work done on the system in going from $A \to B \to C$ is $50 \, J$ and $20 \, cal$ of heat is given to the system. The change in internal energy between $A$ and $C$ is ...... $J$.

$A$ system performs work $\Delta W$ when an amount of heat $\Delta Q$ is added to the system. The corresponding change in the internal energy is $\Delta U$. Which of the following is a unique function of the initial and final states (irrespective of the mode of change)?