Figure shows a cyclic process performed on one mole of an ideal gas. A total of 1000J of heat is withdrawn from the gas in a complete cycle. The magnitude of work done on/by the gas in joule, during the process $B\to C$ is 10x find x. Given R=8.3 J $mo{l}^{-1}{K}^{-1}$.

For a cyclic process,  $\Delta U=0$
$\Rightarrow Q_{cycle}=W_{cycle}$     ….   (1)
Where,   $W_{cycle}=W_{A\to B}+W_{B\to C}+W_{C\to A}$    ….  (2)
Process ${ }_{C\to A}$  is isochoric, hence   $W_{C\to A}$=0
Process  ${ }_{A\to B}$ isobaric, as its T-V graph is a straight line
Passing through origin
In an isobaric process, work done is  $W_{A\to B}=P(V_B-V_A)=nR(T_B-T_A)$
$\Rightarrow W_{A\to B}=1\times 8.3(400-300)=830J$ …. (3)
$W_{A\to B}$  is positive, so expansion of gas takes place.
From the equations 1,2,3 we get
$-1000=830+ W_{B\to C}+0$

$W_{B\to C}=-1830J$