Question

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.

Answer 1

105146 Pa

Step-by-step explanation:

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

• Downward Pressures:

1. Pressure exerted by the compressed spring (Pspring)
2. Pressure due to weight of the piston (Pw)
3. Atmospheric pressure (Patm)

• Upward Pressures:

1. 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