Question

In the given graph an ideal gas changes its state from $A$ to state $C$ by two paths $ABC$ and $AC$. The internal energy of gas at $A$ is $10J$ and the amount of heat supplied in path $AC$ is $200J$. The internal energy $\left(inJ\right)$ of gas at $C$ is $6k^2$. What is the value of $k$?

Answer 1

The first law of thermodynamics states that:

$\delta Q=\Delta U+w=\Delta U+\int PdV$

Work done = $\int PdV$ = area under graph between A and C

Area under graph $=60J$

Given that $\delta Q=200J$

i.e. $\Delta U=140J$

$\Delta U=U_2-U_1=140J=U_2-10J$

i.e. $U_2=150J$

$\Rightarrow 6k^2=150$

$\Rightarrow k=5$