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

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

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.

          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

          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

        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

an ion is a charged atom or molecule. it is charged because the number of electrons do not equal the number of protons in the atom or molecule. an atom can acquire a positive charge or a negative charge depending on whether the number of electrons in an atom is greater or less then the number of protons in the atom.

the independent variable, or the one that is intentionally manipulated is the speed.