Question

Given the graph below which shows the pressure and volume of a gas as it goes through cyclic process $LMNL$, how much heat is gained by the gas as it goes through the process $LM$ (NOT the whole cycle)?
The change in internal energy during process $LM$ is $1000J$

• A. $1000J$
• B. $2000J$
• C. $3000J$
• D. $2500J$
• E. $5000J$

Answer 1

The correct option is C $3000J$

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

From figure, $PM=1\times {10}^5$ Pa $QL=7\times {10}^5$ Pa $PQ=5\times {10}^{-3}$ $m^3$

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

$⟹$ $W_{LM}=\frac{1}{2}\times [PM+QL]\times PQ=\frac{1}{2}\times \left[\right(1+7)\times {10}^5]\times 5\times {10}^{-3}=+2000$ J

Change in internal energy $\Delta U_{LM}=1000$ J

Using $Q_{LM}=\Delta U_{LM}+W_{LM}$

$\therefore$ $Q_{LM}=1000+2000=3000$ J