A gas is confined in a 0.43 m - diameter cylinder by a piston, on which rests a

Question

A gas is confined in a 0.43 m - diameter cylinder by a piston, on which rests a weight. The mass of the piston and weight together is 125 kg. The local acceleration of gravity is 9.811 m/s^2, and the atmospheric pressure is 101.04 kPa. What is the force (in N) exerted on the gas by the atmospheric pressure, the piston and the weight (you may assume that there is no friction between the piston and the cylinder)? If the gas in the cylinder is heated, it expands, pushing the piston and weight upward. If the piston and weight are raised 0.68 m, what is the work done by the gas (in kJ)?

Explanation / Answer

Q5.

k)

Force exerted on gas by (atm + piston + weight)

Patm = 101.04 kPa = 101040 Pa

Ppiston + Pweight = W(piston + weight)/A = m*g/A, where m = mass of piston + weigth

Pmaterial = Ppiston + Pweight = m*g/A

Pm = (125 kg) * (9.8 m/s2) / (A)

A = PI*(R^2) = PI/4 * D^2

A = 3.14159 / 4 * (0.43^2) = 0.14521 m2

Pm = (125 kg) * (9.8 m/s2) / (0.14521 m2)

Pm = 125 *9.8/0.14521 = 8436.058 Pa

Pt = 8436.058 Pa + Patm = 8436.058 Pa + 101040 Pa

Pt = 109476.058 Pa

Now, we need the force

P = F/A

F = P*A

F = 109476.058 Pa * (0.14521 m2)

F = 109476.058 *0.14521 = 15897.01838 N

F = 15897.01838 N (exerted on gas)

l)

W = F*d

d = 0.68 m

F = 15897.01838 N

W = (15897.01838N )*(0.68 N) = 10809.972 J

W = 10809.972 J = 10809.972/1000 kJ = 10.81 kJ

W = 10.81 kJ

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