Work done by Octane Combustion Engine

[SniffLimit]

Homework Statement

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 C_P (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.

Homework Equations

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)
V_i = 0.4996 m³

(500,000 Pa) V = 67 (8.314) (2662.43)
V_f = 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...

 

[berkeman]

Whoops, I solved it...

LOL. Welcome to the PF!

 

[Borek]

Yeah, sometimes just organizing your thoughts to post the question helps.

Feel free to try again next time you have problems with a question