A gas is contained in a vertical, frictionless piston-cylinder device. The piston has a mass of mpiston = 2 kg and a cross-sectional area of Apiston = 30 cm2. A spring above the piston is compressed by s = 2.5 mm and has a spring constant k = 38 kN m. a) If the atmospheric pressure is p[infinity] = 1 atm, determine the initial pressure p1 inside the cylinder. Heat is added to the system until the piston moves an additional 10 mm.

105146 Pa

Explanation:

1) We will make a Free-Body Diagram representing all the upward and downward pressures exerted on the piston.

Downward Pressures: Pressure exerted by the compressed spring (Pspring) Pressure due to weight of the piston (Pw) Atmospheric pressure (Patm) Upward Pressures: Initial pressure inside the cylinder. (P1)

2) We will formulate an equation balancing all upward and downward pressures.

P1 = Patm + Pw + Pspring

3) We will calculate each of the pressures separately.

Pspring

P = F/A

F = ks

k = 38*1000 = 38000 N m

s = 2.5 / 1000 = (2.5x10^-3) m

F = 38000 * (2.5x10^-3) = 95 N

A = 30/10000 = (30x10^-4) m2

P = 95 / (30x10^-4)

Pspring ≅ 3167 Pa

Pw

P = F/A

F = W = mg

W = 2*9.81 = 19.62 N

A = 30/10000 = (30x10^-4) m2

P = 19.62 / (30x10^-4)

Pw = 654 Pa

Patm

P = 1atm = 101325 Pa

Patm = 101325 Pa

4) We will add all the downward pressures to reach the final answer (initial pressure inside the cylinder).

P1 = Patm + Pw + Pspring

P1 = 101325+654+3167

P1 = 105146 Pa