The drawing shows an ideal gas confined to a cylinder by a massless piston that

Question

The drawing shows an ideal gas confined to a cylinder by a massless piston that is attached to an ideal spring. Outside the cylinder is a vacuum. The cross-sectional area of the piston is A = 2.50 × 10-3 m2. The initial pressure, volume, and temperature of the gas are, respectively, P0, V0 = 6.00 × 10-4 m3 and T0 = 273 K, and the spring is initially stretched by an amount x0 = 0.094 m with respect to its unstrained length. The gas is heated, so that its final pressure, volume, and temperature are Pf, Vf and Tf and the spring is stretched by an amount xf = 0.10 m with respect to its unstrained length. What is the final temperature of the gas?

Explanation / Answer

You don't show the picture, but since the spring stretches when the gas is heated, I guess the spring goes from the center of 1 end of the cylinder over to the center of the piston, and is as long as the cylinder itself. P0 V0/ T0 = Pf Vf/ Tf Vf/V0 = 1.11/1.084 = 1.023985 We can find Pf/P0, because P = F/A = kx/A; thus Pf/P0 = 0.10/0.094 = 1.063 So, Tf = T0 times (Pf/P0)(Vf/V0) = (273 K)(1.023985)(1.063) = 297.39K

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