A system goes from $P$ to $Q$ by two different paths in the $P – V$ diagram as shown in figure. Heat given to the system in path $1$ is  $1000\,J$ . The work done by the system along path $1$ is more than path $2$ by  $100\,J$ . What is the heat exchanged by the system in path $2$ ?

In pressure-volume diagram given below, the isochoric, isothermal, and isobaric parts respectively, are

A gas is taken through the cycle $A\to B\to C\to A$ as shown. What is the net work done by the gas …… $J$ $?$

$n$ moles of a van der Waals' gas obeying the equation of state $\left(p+\frac{n^2 a}{V^2}\right)(V-n b)=n R T$, where $a$ and $b$ are gas dependent constants, is made to undergo a cyclic process that is depicted by a rectangle in the $p-V$ diagram as shown below. What is the heat absorbed by the gas in one cycle?

One mole of an ideal gas goes from an initial state $A$ to final state $B$ via two processes : It first undergoes isothermal expansion from volume $V$ to $3\, V$ and then its volume is reduced from $3\, V$ to $V$ at constant pressure. The correct $P-V$ diagram representing the two processes is