Work done by piston in combustion chamber with fuel energy input

[nlsed]

Homework Statement

The Internal energy of fuel in a combustion chamber increases by 75J due to 130J of heating. How much work can be done by the piston? How far does the piston move while pushing with 5000N of force?

Homework Equations

The Attempt at a Solution

Since they gave us the info to find efficiency i divided 75J by 130J and got 57.7% eff. I plugged that into (e= w/Q_H) and got work = 75.01J and i plugged it into w=F *(delta x) and got .015m. I'm not sure if this is right, but the units seem to be correct.

 

[Redbelly98]

The Attempt at a Solution

Since they gave us the info to find efficiency i divided 75J by 130J and got 57.7% eff. I plugged that into (e= w/Q_H) and got work = 75.01J and i plugged it into w=F *(delta x) and got .015m. I'm not sure if this is right, but the units seem to be correct.

Not quite.

As you said, efficiency is

e = w/Q_H​

However, you have used ΔU, not w, to calculate e=57.7%. So that's incorrect.

What is another equation that relates U, W, and Q? It should be in your textbook, early in the section or chapter on thermodynamics.