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

Answer 1

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


By first law of thermodynamics,

$\Delta Q_{AC}=\Delta W_{ACB}+\left(\Delta U\right)$

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

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

Now for the path $ADB$,

$\Delta Q_{ADB}=\Delta U_{ADB}+\Delta W_{ADB}$

As internal energy is a point function, $\therefore \Delta U_{ACB}=\Delta U_{ADB}$

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

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