The cylinder in the figure ( Figure 1 ) has a moveable piston attached to a spri

Question

The cylinder in the figure(Figure 1) has a moveable piston attached to a spring. The cylinder's cross-section area is 10 cm2, it contains 0.0057mol of gas, and the spring constant is 1500 N/m. At 19?C the spring is neither compressed nor stretched. The cylinder in the figure(Figure 1) has a moveable piston attached to a spring. The cylinder's cross-section area is 10 cm2, it contains 0.0057mol of gas, and the spring constant is 1500 N/m. At 19?C the spring is neither compressed nor stretched. The cylinder in the figure(Figure 1) has a moveable piston attached to a spring. The cylinder's cross-section area is 10 cm2, it contains 0.0057mol of gas, and the spring constant is 1500 N/m. At 19?C the spring is neither compressed nor stretched. The cylinder in the figure(Figure 1) has a moveable piston attached to a spring. The cylinder's cross-section area is 10 cm2, it contains 0.0057mol of gas, and the spring constant is 1500 N/m. At 19?C the spring is neither compressed nor stretched. Part A How far is the spring compressed if the gas temperature is raised to 150?C? The cylinder in the figure(Figure 1) has a moveable piston attached to a spring. The cylinder's cross-section area is 10 cm2, it contains 0.0057mol of gas, and the spring constant is 1500 N/m. At 19?C the spring is neither compressed nor stretched. Part A How far is the spring compressed if the gas temperature is raised to 150?C? The cylinder in the figure(Figure 1) has a moveable piston attached to a spring. The cylinder's cross-section area is 10 cm2, it contains 0.0057mol of gas, and the spring constant is 1500 N/m. At 19?C the spring is neither compressed nor stretched. How far is the spring compressed if the gas temperature is raised to 150?C?

Explanation / Answer

A = the cylinder's cross-section area = 10 cm2 = 0.0010 m2

P1i = P2i

==> n R T1/V1 = P_atmosphere

==> 0.0057 * 8.314 * (19+273)/V1 = 1.01 x 10^5 Pa

==> V1 = 1.3701e-4 m3

==> initial length of the cylinder = L = V1/A = 1.3701e-4/0.0010 = 0.13701 m

P1f = P2f

==> n R T2/V2 = P_atmosphere + (k dL)/A

==> n R T2/((L+dL)*A) = P_atmosphere + (k dL)/A

==> 0.0057 * 8.314 * (150+273)/((0.13701+dL)*0.0010) = 1.01e5 + 1500*(dL)/0.0010

==> dL = 0.0186 m

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