Question

a pump is driven by burn methane. find volume of methaneat 27.5degrees, 2.25bar that must be burned ib excess of oxygento produce enough enegy to compress 10e6 L of gas to 3500L at 250bar. assume 40% of energy of combustion is lost as heat

Answer 1

amount of work to be done by system = pressure *change in volume [since it's a isobaric process]

=250*0.986*(1000000-3500) [since 1 bar = 0.986 atm]

= 246.5*10⁶ atm-lit

=246.5*10⁶*101.325 J =24976.6125*10⁶ J

Methane produces 50.1 Kj of heat energy per gram

Mass of methane required = 24976.6125*10⁶ /50100 = 0.498 *10^6 grams = 498 Kg

as 40% of energy is getting wasted we have to additionally burn 40%

mass of methane required = 498/1-0.4 = 830 Kg

number of moles of methane = 830000/16 =51875 moles

using ideal gas equation,

Volume V = nRT/P = 51875*300.5*8.31446261815324×10⁻²/2.25 = 576010 Lit