How much work is done to expand a 10-cm diameter cylindrical chamber at 1 atm from a length of 10 cm to a length of 20 cm?

Question

Quizplus · Accepted Answer

The work done to expand a chamber is given by the equation W = PΔV, where P is the pressure, and ΔV is the change in volume. For a cylindrical chamber, the volume is given by V = πr^2h, where r is the radius and h is the height. Since the radius remains constant at 5 cm (half the diameter), we can simplify the equation to V = πr^2Δh, where Δh is the change in height.

To find Δh, we subtract the initial height of 10 cm from the final height of 20 cm, giving Δh = 10 cm. Plugging this into the equation for volume, along with the radius of 5 cm, we get ΔV = π(5 cm)^2(10 cm) = 785.4 cm^3.

Finally, we can calculate the work done using W = PΔV. Since the pressure is given as 1 atm, we have W = (1 atm)(785.4 cm^3) = 79.3 J. Therefore, the answer is (C).

How Much Work Is Done to Expand a 10-Cm Diameter