Question

In the given graph an ideal gas change its state from A to state C by two paths ABC and AC. If the work done in path ABC is $5k^2$ (in J). What is the value of $k$ ?

Answer 1

Area under the P-V graph gives the work done by the gas during that process.

From graph, $OD=15-5=10m^3$

Process AC :

$W_{AC}=$ Area of trapezium AODC $=\frac{1}{2}\times (AO+CD)\times OD$

$\therefore$ $W_{AC}=\frac{1}{2}\times (4+8)\times 10=60J$

Process ABC :

$W_{AB}=0$ $(\because V=constant)$

$W_{BC}=OD\times OB=10\times 8=80J$

$⟹W_{ABC}=0+80=80J$

$\Rightarrow 5k^2=80$

$\Rightarrow k=4$