Question

Chapter 14, Problem 26 GO 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 x 103 m². The initial pressure, volume, and temperature of the gas are, respectively, Po, Vo = 6.00 x 10-4 m and To = 273 K, and the spring is initially stretched by an amount Xo = 0.097 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 xp = 0.14 m with respect to its unstrained length. What is the final temperature of the gas? - Piston Tp = the tolerance is +/-2% Click if you would like to Show Work for this question: Open Show Work

Answer 1

Given data o A = P.5 X10-3 m? Vo = 6410-4 m3 To = 273k Xo = 0.097 m xf = 0.14 m

» Piston moved by. Dx = x - xo = 0.14 - 0.097 2. DX = 0.043 m. - In the heating process, Que to the displacement of the piston the volume of the Enclosed gas increa- sed by AV. DARI A 0.043 X 2,5 x 107 do Ave 10.75 X 10-5 m3 final volume V = Vot av = (6 x 10-4) + (1.075 X10-4)

oo Ug = 7.075 X10-4 m3 70075 x 104 6 x 10-4 = 1.1991 » Hence, Ts = To* ( 9.) * ( T5 = 243 * ( ) + (1.1991) To solve four Pf a Tf = 273 * 91

Kх 3.14 О.097 :. Р. Г. 44.32 эҒмот &q, О. Тg = (2+3) + (1.4432) (1.14) 2. Т = 4.4. 599 К