A gas fills the right portion of a horizontal cylinder whose radius is 4.10 cm.
ID: 1497305 • Letter: A
Question
A gas fills the right portion of a horizontal cylinder whose radius is 4.10 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 16.0 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.
Unstrained spring Pin IWIINI
Explanation / Answer
The volume of the cylinder is V = AL where A is the cross-sectional area of the piston and L is the length.
We know P1 V1 = P2 V2 so that the new pressure P2 can be found.
P2 = P1*(V1/V2) = P1(A1L1/A2L2) -----------(A1 = A2)
after expansion chanber length doubles. as area of cross-section of cylinder is same
so L2 = 2L1
P2 = P1*(L/2L) = P1 / 2 = (1.01 x 10^5 N) / 2 = 5.05 x 10^4 pa
The force on the piston and spring is
F = P2*A = (5.05 x 10^4 x 3.14 x 0.041^2) = 266.556 N
The spring constant is k = F/x
K = 266.556 / 0.16 = 1665.976 N/m
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