Question

In the given figure, the initial and final states of a gas are shown by points $i\text{and}f$. The internal energy of the gas at $i$ is $10\text{J}$. For the path $iaf:Q=50\text{J}\text{and}W=20\text{J}$. If for the path $ibf:Q=36\text{J}$, then the value of $W$ for this path will be equal to

• A. $4\text{J}$
• B. $12\text{J}$
• C. $18\text{J}$
• D. $6\text{J}$

Answer 1

The correct option is D $6\text{J}$

In both the process, initial and final state are same.

As the internal energy is a state function,

$\Delta U_{iaf}=\Delta U_{ibf}$

$\Rightarrow Q_{iaf}-W_{iaf}=Q_{ibf}-W_{ibf}$

$\Rightarrow 50-20=36-W_{ibf}$

$\Rightarrow W_{ibf}=6\text{J}$

Hence, option $\left(D\right)$ is correct.