A gas fills the right portion of a horizontal cylinder whoseradius is 5.75 cm. T

Question

A gas fills the right portion of a horizontal cylinder whoseradius is 5.75 cm. The initial pressure of the gas is 2.72 x105 Pa. A frictionless movable piston separates the gasfrom the left portion of the cylinder that is evacuated andcontains an ideal spring, as the drawing shows. The piston isinitially held in place by a pin. The spring is initiallyunstrained, and the length of the gas-filled portion is 25.4 cm.When the pin is removed and the gas is allowed to expand, thelength of the gas-filled chamber doubles. The initial and finaltemperatures are equal. Determine the spring constant of thespring.

Explanation / Answer

   if A and L are the cross sectional area andlength of the piston then the volume of the cylinder is    given by    V = A L    as P V = constant we can write    P1 V1 = P2V2    P2 = P1(V1/ V2)   (as A1 =A2)         = P1A1L1 / A2L2         =P1 L1 / L2    P2 = (1.01 x 105 Pa) (L / 2L)        = ..........Pa    the force on the piston and the spring willbe    F = P2 A       = ....... N    as we know that    k = F / x       = F / (0.254 m)       = ........ N / m         =P1 L1 / L2    P2 = (1.01 x 105 Pa) (L / 2L)        = ..........Pa    the force on the piston and the spring willbe    F = P2 A       = ....... N    as we know that    k = F / x       = F / (0.254 m)       = ........ N / m

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