Question

The cylinder in the figure(Figure 1) has a moveable piston attached to a spring. The cylinder's cross-section area is 10 cm”, it contains 0.0051 mol of gas, and the spring constant is 1500 N/m. At 17 °C the spring is neither compressed nor stretched. Part A How far is the spring compressed if the gas temperature is raised to 120 °C? Express your answer to two significant figures and include the appropriate units. Ar = 0.94 cm cm Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining Provide Feedback Figure < 1 of 1 > 1500 N/m A = 10 cm

Answer 1

The answer for above problem is explained below.

By using Ideal gas equation, . P; V; = nRT; - Vi = nRT; 3 V 0.0051 mol X 8.314 Jmoiik" x (273+17)k 1.013X 105 Pa = V; = 1, 21386 x 104 mp3 And sv = Ax a sve 10 x[17m}x = av = [10 x 104 m²] => or = (0.001 m) x 4 0 And AP = kx =) sp = (1500 N/m 2x 0.001 m² = DP = [15x105 N/mm] x —©

And ff f = nR If ) Pi + DP) (V; + Ov) = nRTH z) 1.013 x16 Pa + (15 x10 9 Nov x)] [ 1. 21386 x104m? + 2 - (0.001m2)x] = 0.00 51 mol x 8. 314 3 moi'k"* (2737 120]k 0.00 51 mol X 8. 314 J mol'k * 120k - 12.2964 Pam² + (10103 Pam²) x + [182.079 N] + (1500 N/m] x2 = 16.663 = 11500 N/m] x² + (283.379 hPa m²Jx - 4.3666 Pam?=0 . By solving above equation, We get, x=0.0143 m