Question

Given the graph above which shows the pressure and volume of a gas as it goes through cyclic process $XYZX$, how much work is done by the gas as it goes through the process $XY$ (NOT the whole cycle?

• A. $1200J$
• B. $3000J$
• C. $3200J$
• D. $1800J$
• E. $600J$

Answer 1

Answer: (B)

$3000J$

Area under the PV graph gives the work done by the gas during that process.

From figure, $PY=3\times {10}^5$ Pa $QX=7\times {10}^5$ Pa $PQ=6\times {10}^{-3}$ $m^3$

$\therefore$ Work done by gas during $XY$, $W_{XY}=$ Area of trap(XYPQ)

$⟹$ $W_{XY}=\frac{1}{2}\times [PY+QX]\times PQ=\frac{1}{2}\times \left[\right(3+7)\times {10}^5]\times 6\times {10}^{-3}=3000$ J