In the $P-V$ diagram shown,the gas does $5 \, J$ of work in the isothermal process $ab$ and $4 \, J$ of work in the adiabatic process $bc$. What will be the change in internal energy of the gas in the straight path $c$ to $a$ (in $, J$)?

$2$ moles of an ideal monoatomic gas is carried from a state $(p_{0}, V_{0})$ to state $(2 p_{0}, 2 V_{0})$ along a straight line path in a $p-V$ diagram. The amount of heat absorbed by the gas in the process is given by

One mole of an ideal diatomic gas expands from volume $V$ to $2V$ isothermally at a temperature $27^{\circ} C$ and does $W$ joule of work. If the gas undergoes the same magnitude of expansion adiabatically from $27^{\circ} C$ doing the same amount of work $W$, then its final temperature will be (close to) . . . . . . ${ }^{\circ} C$.

Two identical samples of a gas are allowed to expand $(i)$ isothermally and $(ii)$ adiabatically. The work done is:

Match List-$I$ with List-$II$.

List-$I$	List-$II$
$(A)$ Isothermal	$(I)$ $\Delta W = 0$
$(B)$ Adiabatic	$(II)$ $\Delta Q = 0$
$(C)$ Isobaric	$(III)$ $\Delta U \neq 0$
$(D)$ Isochoric	$(IV)$ $\Delta U = 0$

Choose the correct answer from the options given below:

In thermodynamics,heat and work are