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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.

Respuesta :

Answer:

105146 Pa

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