Question

(II) Sketch a PV diagram of the following process: 2.5 L of ideal gas at atmospheric pressure is cooled at constant pressure to a volume of 1.0 L, and then expanded isothermally back to 2.5 L, whereupon the pressure is increased at constant volume until the original pressure is reached.

Short answer

The PV diagram of the process is shown below.

Step-by-step solution

Concepts 

The process is called isobaric as the pressure is constant.

For the isothermal expansion, the gas follows Boyle's law.

Given data 

The initial volume of the gas is \({V_1} = 2.5\;{\rm{L}}\).

The initial pressure is\({P_1} = 1{\rm{ atm}}\).

The volume of the gas after compression at constant pressure is \({V_2} = 1.0\;{\rm{L}}\).

Suppose after the first compression of the gas, the volume and the pressure are \(\left( {{P_1},{V_2}} \right)\).

Again, suppose after the isothermal expansion, the pressure and volume of the gas are\(\left( {{P_2},{V_1}} \right)\).

PV diagram

For the isothermal process,

\(\begin{array}{c}{P_2}{V_1} = {P_1}{V_2}\\{P_2} \times \left( {2.5\;{\rm{L}}} \right) = \left( {1{\rm{ atm}}} \right) \times \left( {1.0\;{\rm{L}}} \right)\\{P_2} = 0.4\;{\mathop{\rm atm}\nolimits} .\end{array}\)

Therefore, the PV diagram formed is shown below: