Question

A frictionless free piston-cylinder device contains 5125 g of CH4 (methane) at -70.0°C. The initial volume the CH4 occupies is 145 L. Heat is added to the CH4 until a final volume of 500 L is achieved. Determine the final temperature of the CH4 using: a) The ideal gas equation. (3 marks) b) The compressibility factor approach. (5 marks)
please show work

Answer 1

Solution to question (1).

Given m=5125 g T,= - 70 c= 10+273-15=203.15 = 145x10 m - soox 103 m3 T2 = ? (a) By using ideal gas equation. PV = P₂ V₂ MRT MRT2 P, = P2 ( Frictionless free piston) 145X10 10-3 203.15 50oxio Tz T = 700.52k T = Folk (6) compressi actor approach. - for methane : R=0.5182 kJ/kgik Por = 4.644 MPa P = MRT To - 19101k. vor = 0.0993 m/kmol. - 5.125X0.5182x103 X 203. M = 16.043 kg/knol- 145x103 P = 3.72 x 10 Pa = 3.72 MPa

Reduced pressure: - PR= R - 3072 ² = 0.8019 Per 4.64 203-15 19. - 1.063 Teto 203.15 1.063 using charts for methane, at PR = 0.8019 and Te = 1:063, the compressibility factor is, : 2=0.16 The temperature is. T2 = P2 V2 [P₂ = P, = 3.42 MP a] mZR = 3.72x10x500x10 5.125 *0.76 * 0.5182x10² To=921.5k