Question

A 1.0-L volume of air initially at 3.5 atm of (gauge) pressure is allowed to expand isothermally until the pressure is 1.0 atm. It is then compressed at constant pressure to its initial volume, and lastly is brought back to its original pressure by heating at constant volume. Draw the process on a PV diagram, including numbers and labels for the axes.

Answer 1

The student is asking to illustrate a thermodynamic cycle on a PV diagram involving isothermal expansion, isobaric compression, and isochoric heating for an ideal gas.

Step-by-step explanation:

The student is describing a thermodynamic cycle consisting of three processes for an ideal gas: (1) isothermal expansion from 3.5 atm to 1.0 atm, (2) isobaric compression back to the initial volume, and (3) isochoric increase in pressure back to the initial value. To illustrate these processes on a PV diagram:

• Mark the initial point at 1.0 L and 3.5 atm. Draw an isothermal curve (hyperbolic shape) that decreases in pressure to 1.0 atm and increases in volume until the new state is reached. This first process shows the isothermal expansion.
• From this state, draw a vertical line straight down to indicate isobaric compression back to the original volume of 1.0 L.
• Finally, draw a horizontal line back to the initial pressure of 3.5 atm, representing isochoric heating.

Be sure to label the axes with 'Pressure (atm)' on the y-axis and 'Volume (L)' on the x-axis, and indicate the states and processes with appropriate numbers and letters.