Question

6. A cylinder contains 10 kg of air (ideal gas) and 200 kPa, is maintained at 27 C, and its pressure doubles, the cylinder rises 0.035, determine: initial volume of the tank, final volume, the diameter of the cylinder and the work done by gas.

Answer 1

6 soln Given data, mass of air, m=10kg Initial pressure, P, = 200kPa = 20000opa Temperature , T = 27C = 27+ 273 Final Pressure, P2 = 4000oopa - 300K Rise in height, Ah=0.035m Let V and V2 vite dhi be the initial and final volume V₂ = 7 daha > where, d is the diameter of cylinden From ideal gas equation PV=MRT where, constant R is the individual and For air R=287.05 gas J/kg k Now, For initial state Pivo =MRT Vi= MRT Vi = 10x287.05x 300 200OOD V=4.31 m3 Fon constant temperature process Pivi = P2 V2 Pivi 200000X 4.31 V₂ = P2 4ooooo V2 = 2.16 m²

V2 = v= I dha - 7 dni V2 y = Il d? ( 22 - h) 4.31-2016=t d² ph d²= 4x2.15 3.148 0.035 d² - 78.253 Id=8.846m For isotren mal process, work done by the is given by, W-Pivi Inv2 V 2016 W = (200000 x 4.31)xin 4.31 W =- 595495.19 N Negative sign indicates that work is done by the gas. w = 5.95 +105N