A gas fills the right portion of a horizontal cylinder whose radius is 4.05 cm.

Question

A gas fills the right portion of a horizontal cylinder whose radius is 4.05 cm. The initial pressure of the gas is 2.15 x 105 Pa. A frictionless movable piston separates the gas from the left portion of the cylinder that is evacuated and contains an ideal spring, as the drawing shows. The piston is initially held in place by a pin. The spring is initially unstrained, and the length of the gas-filled portion is 29.0 cm. When the pin is removed and the gas is allowed to expand, the length of the gas-filled chamber doubles. The initial and final temperatures are equal. Determine the spring constant of the spring.

Explanation / Answer

Since temperature remians constant

Therefore P1*V1 = P2*V2 ; where P & V are pressure and volume respectively

or, 2.15*105*pi*4.052*29 = P2*pi*4.052*58

or, P2 = 1.075*105 Pa

Thus, pressure difference = P1-P2 = 1.075*105 Pa

Area of piston = pi*r2 = 3.14*0.04052 = 5.1504*10-3 m2

Force = pressure*area = (1.075*105)*(5.1504*10-3) = 553.668 N

Now, let the spring constant = k

Thus, force = k*x

or, k = 553.668/(0.58-0.29) = 1909.2 N/m

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