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

Question

The drawing shows an ideal gas confined to a cylinder by amassless piston that is attached to an ideal spring. Outside thecylinder is a vacuum. The cross-sectional area of the piston isA = 2.50 × 10-3 m2. Theinitial 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 amountx0 = 0.086 m with respect to its unstrainedlength. The gas is heated, so that its final pressure, volume, andtemperature are Pf, Vf andTf and the spring is stretched by an amountxf = 0.11 m with respect to its unstrainedlength. What is the final temperature of the gas?

Explanation / Answer

A = 2.50 × 10-3 m2.P0, V0 = 6.00 ×10-4 m3, T0 = 273 K,x0 = 0.086 m xf = 0.11 m, find final temperature of the gasTf P0 = kx0/A, Pf = kxf/A,Vf = V0 + A(xf - x0) =6.60 × 10-4 m3 use P0V0/T0 =PfVf/TfTf =(xf/x0)(Vf/V0)*T0= 384 K

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