Question

In the figure, an ideal gas changes its state from state $A$ to state $C$ by two paths $ABC$ and $AC$.
The internal energy of gas of $A$ is $30J$ and the amount of heat supplied to change its state to $C$ through path $AC$ is $210J$. Calculate the internal energy of gas at $C$.

Answer 1

Process $A$ to $C$
$Q=210J$
Work done $W_{AC}=$ area under $AC$
$=(10\times 4)+\left(\frac{10\times 4}{2}\right)=60J$
From $Ist$ law of thermodynamics.
$△U=Q-W_{AC}$
$\Rightarrow U_C-U_A=210-60$
$\therefore U_C=U_A+150=30+150=180J$.