Question

Draw a cylinder with a movable piston containing six molecules of a liquid. A pressure of 1 atm is exerted on the piston. Next draw the same cylinder after the liquid has been vaporized. A pressure of one atmosphere is still exerted on the piston. Is work done on the system or by the system?

Short answer

Answer: The work done is positive and is done by the system.

Step-by-step solution

Understand the initial condition of the system

The problem mentions a cylinder with a movable piston containing six molecules of a liquid. The pressure exerted on the piston is 1 atm. So, initially, the system is in the liquid state under a pressure of 1 atm.

Visualize the final condition of the system

The problem asks us to consider the same cylinder after the liquid has been vaporized. This means the liquid has turned into a gaseous state but the pressure exerted on the piston remains the same, 1 atm.

Analyze the work done

In a thermodynamic process, work done on the system is defined as the force applied multiplied by the displacement of the piston. We know that pressure is force per unit area, and therefore, we can say work done is equal to pressure multiplied by volume change. Mathematically, work done (W) = Pressure (P) × Change in volume (∆V).

Compare the initial and final volume of the system

In this case, the pressure remains the same before and after the vaporization process (1 atm). However, since the liquid has vaporized, the volume occupied by the molecules has increased. This implies that the final volume (V2) will be greater than the initial volume (V1).

Calculate work done

Since there's a change in volume, we can conclude that there's work done in the process. As ΔV = V2 - V1, and we know that V2 > V1, ΔV will be positive. Applying the formula, we have W = P × ΔV, where P is constant at 1 atm and ΔV is positive. Since W is positive, it means that work is done by the system (since the system has expanded).

Conclusion

After the liquid is vaporized and the pressure is maintained at 1 atm, the volume of the system increases, resulting in positive work done by the system.