Answer to Question #233429 in Civil and Environmental Engineering for Adeel

Question

6. Gas fills a cylinder fitted with a frictionless piston. The initial pressure and volume are 40 MPa and 0.05 dm3 respectively. The gas expands reversibly and polytropically to 0.5 MPa and 1 dm3 respectively. Calculate the index of expansion and the work done. 

Answer 1

p₁ =40MPa

V₁ =0.05dm³

p₂ =0.5MPa

V₂ =1dm³

p₁V₁ⁿ = p₂V₂ⁿ

(40/0.5) = (1/0.05)ⁿ

80 = 20ⁿ

n = 1.463

W=p₂V₂-P₁V₁/n-1

=(0.5x10⁶)x(1x10^-3)−(40x10⁶⁾x(0.05x10^-3)/0.463

=-3.24KJ