Question

If the gas in the cylinder is heated, it expands, pushing the piston and weight upward. If the piston and weight are raised 0.83 m, what is the work done by the gas in kJ

Answer 1

15.848 kJ

Step-by-step explanation:

A gas is confined in a 0.47 m diameter cylinder by a piston, on which rests a weight. The mass of the piston and weight together is 150 kg. The local acceleration of gravity is 9.813m⋅s−2,and atmospheric pressure is 101.57 kPa

Solution:

Given that the diameter (d) = 0.47 m, the mass of piston and weight (m) = 150 kg, the acceleration due to gravity (g) = 9.813 m/s² and the atmospheric pressure (
`P_(atm)`) = 101.57 kPa = 101.57 * 10³ Pa

The area (A) = πd²/4 = π * 0.47² / 4 = 0.1735 m²

The force due to atmosphere (Fa) =
`P_(atm)` * A = 101.57 * 10³ * 0.1735

Fa = 17622 N

Force due to piston and mass (
`F_(pm)`) = m * g = 150 * 9.813 = 1471.95 N

The total force exerted (F) =
`F_(pm)` + Fa

F =
`F_(pm)` + Fa

F = 17622 N + 1471.95 N

F = 19093.95 N

The work done by the gas (W) = total force * change in distance

W = F * Δx

W = 19093.95 N * 0.83 m

W = 15848 J

W = 15.848 kJ