A gas fills the right portion of a horizontal cylinder whose radius is 5.80 cm.

Question

A gas fills the right portion of a horizontal cylinder whose radius is 5.80 cm. The initial pressure of the gas is 1.01 × 105 Pa. A frictionless movable piston separates the gas from the left portion of the cylinder, which is evacuated and contains an ideal spring, as the figure 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 17.0 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

gas expands isothermally (T is same), so from gas equ
P1V1 = P2 V2
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after expansion chanber length doubles. as area of cross-section of cylinder is same
so V2 = 2V1
P2 = P1V1/V2 = P1/2 = 1.01*10^5/2
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finally force exerted on piston = P2* area of crossection
F = [1.01*10^5/2]* pi r^2
F = [1.01*10^5/2]*3.14* (0.0580)^2
F = 213.37 Newton
this force compresses the spring
|F| = k *x for spring (where x = 17 cm = 0.17 m, as length doubled whereby compression from unstrained position is 17 cm)
k = 213.37 / 0.17 = 1255.11 N/meter

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