There is an insulated internal combustion engine fueled by one mole of octane. It operates at a constant pressure of 5.0 bar. The initial temperature is 200°C. Calculate the heat exchanged with the surroundings, the Δh for the gas, the final temperature, the work performed by the gas, and and the Δu for the gas.
I'm given the balanced equation:
C8H18 + 12.5 O2 + 50 N2 → 9 H2O + 8 CO2 + 50 N2
I'm also given the enthalpies of formation and the CP (at 298 K) for each product and reactant, but I've already successfully found the final temperature, so I don't think it's necessary to include them here.
I just need to find the work and the Δu at this point.
w = nRΔT
w = -PΔV
Δu = q + w
PV = nRT
The Attempt at a Solution
The heat exchanged with the surroundings is 0. The Δh for the gas is 0. The final temperature is 2662.42 K. I've confirmed that these three answers are correct. To find the work, I think I would just use the work equation above, but I'm not sure what it wants me to plug in for n. Moles of reactants? Moles of products?
I suppose I could use the ideal gas equation to find the volumes at the initial and final temperatures, and then use the other work equation.
(500,000 Pa) V = 63.5 (8.314) (473.15)
Vi = 0.4996 m3
(500,000 Pa) V = 67 (8.314) (2662.43)
Vf = 2.9661 m3
ΔV = 2.466560689 m3
w = (-500,000 Pa) (2.466560689 m3)
w = -1233280.344 J
But how would I go about finding the Δu?
Δu = Δh - PΔV
Whoops, I solved it...