Question

a) An ideal gas is taken through a quasi-static process described by ρ-α 2 with a = 7.50 atm m , as shown in the figure. The gas is expanded to t ce its original volume of 1.00 m3 How much work in is done on the expanding gas in this process? P-aV 1.00 m3 2.00m O (b) What If? How does the work done in part (a) compare to the lowest and highest possible amounts of work that can be done on this gas between the iniial and final states if the pressure always remains between P and Pp and the volume always remains between V and v2 (Enter your answers as percentages of the work done in part (a).) lowest X 100% part (a) Was wnanest. x 100% 0/% part (a)

Answer 1

Given: - pressure, p = alpha v^2 alpha = 7.5 atm/m^6 1 atm = 101.32 times 10^3 pa initial vol, v_i = 1 m^3. Final vol v_f = 2 m^3 work done on expansion: w = -integral^vf_v_i p dN = -integral^vf_v_i alpha v^2 dv w = -alpha/3[v_f^3 - v_i^3] w = -7.5 times 101.325 pa/m^6 times 10^3 [(20 m)^3 - (1.0 m)^3]/3 w = -1.77 mJ

Answer 2