Question

A closed system receives $200\text{kJ}$ of heat at constant volume. It then rejects $100\text{kJ}$ of heat while it has $50\text{kJ}$ of work done on it at constant pressure. If an adiabatic process can be found which will restore the system to its initial state, the work done by the system during this process is

• A. $100\text{kJ}$
• B. $50\text{kJ}$
• C. $150\text{kJ}$
• D. $200\text{kJ}$

Answer 1

The correct option is C $150\text{kJ}$

Given, that system is closed one
$\therefore$ We can infer that $\Delta u_{net}=0$
System is going through isochoric, isobaric and adiabatic process.
$\therefore \Delta u_1+\Delta u_2+\Delta u_3=0----\left(1\right)$
In isochoric process, $W=0\Rightarrow \Delta u_1=Q_1----\left(2\right)$
In isobaric process, $\Delta u_2=Q_2-W_2----\left(3\right)$
In adiabatic process, $\Delta Q=0\Rightarrow \Delta u_3=-W_3----\left(4\right)$
Using $\left(1\right),\left(2\right),\left(3\right)\&\left(4\right)$ we get,
$Q_1+Q_2-W_2-W_3=0$
$\therefore 200+(-100+50)-W_3=0$
$\Rightarrow W_3=150\text{kJ}$