Question

Air in a piston/cylinder arrangement, shown in the figure below is at 200 kPa, 300 K, with a volume of 0.5 $m^3$. When the piston just touches the stoppers, its volume is 1 $m^3$ and the pressure is 400 kPa. The air is heated from the initial state to 1500 K with the help of a 1900 K reservoir.

Choose the correct option from the following:

• A. Piston will touch the stopper, final pressure of air is 500 kPa and work done by air is 150 kJ
• B. Piston will touch the stopper, final pressure of air is 400 kPa and work done by air is 150 kJ
• C. Piston will touch the stopper, final pressure of air is 500 kPa and work done by air is 175 kJ
• D. Piston will not touch the stopper & final pressure is 200 kPa

Answer 1

The correct option is C Piston will touch the stopper, final pressure of air is 500 kPa and work done by air is 175 kJ

Let us suppose that piston just hits the stopper.

So pressure of air becomes

$P_f=400kPa\text{and}{V}_f=1m^3$

From,
$\frac{P_1{V}_1}{T_1}=\frac{P_f{V}_f}{T_f}$

$\frac{200\times 0.5}{300}=\frac{400\times 1}{T_f}\Rightarrow T_f=1200K$

If temperature of air becomes 1200 K, piston will just touch the stopper. Now, since air is heaed to 1500 K, piston will definitely hit the stopper. Let us suppose the pressure of air becomes
$P_2$.

$\frac{200\times 0.5}{300}=\frac{P_2\times 1}{1500}\Rightarrow P_2=500kPa$

$W=\frac{1}{2}\times [P_1+P_f]\times 0.5=175kJ$