Question

A gas can be taken from $A$ to $B$ via two different processes, $ACB$ and $ADB$.


When path $ACB$ is used, $60\text{J}$ of heat flows into the system and $30\text{J}$ of work is done by the system. If path $ADB$ is used, work done by the system is $10\text{J}$. The heat flow into the system in path $ADB$ is:

• A. $100\text{J}$
• B. $80\text{J}$
• C. $20\text{J}$
• D. $40\text{J}$

Answer 1

The correct option is D $40\text{J}$


$\Delta U$ remains same for both paths $ACB$ and $ADB$ as the initial and the final states of both the path are same.

From the first law of thermodynamics,
$\Delta Q_{ACB}=\Delta W_{ACB}+\Delta U_{ACB}$

$\Rightarrow 60\text{J}=30\text{J}+\Delta U_{ACB}$

$\Rightarrow U_{ACB}=30\text{J}$

$\therefore \Delta U_{ADB}=\Delta U_{ACB}=30\text{J}$

Again, using the first law of thermodynamics,
$\Delta Q_{ADB}=\Delta U_{ADB}+\Delta W_{ADB}$

$\Rightarrow \Delta Q_{ADB}=30\text{J}+10\text{J}=40\text{J}$

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