Calculating Work & Displacement of a Piston w/ Fuel Energy

[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.

 

[nlightner]

I would like to provide a more detailed explanation and justification for the solution provided in the attempt.

Firstly, it is important to understand the concept of work and displacement in this scenario. Work is defined as the energy transferred to or from an object by a force acting on the object. In this case, the work done by the piston is equal to the force applied (5000N) multiplied by the displacement of the piston (delta x). This work is done by the piston on the fuel, causing it to increase in internal energy.

Next, we need to consider the efficiency of this process. Efficiency is a measure of how well energy is converted from one form to another. In this case, the efficiency is given as 57.7%, meaning that only 57.7% of the energy input (130J) is converted into work output (75J). This can be expressed mathematically as:

Efficiency = Work output / Energy input

Therefore, we can rearrange the equation to solve for work output:

Work output = Efficiency * Energy input

Substituting the values, we get work output = 57.7% * 130J = 75.01J. This matches the value calculated in the attempt.

Now, to calculate the displacement of the piston, we can use the equation mentioned earlier: work = force * displacement. Rearranging the equation to solve for displacement, we get:

Displacement = Work / Force

Substituting the values, we get displacement = 75.01J / 5000N = 0.015m. This also matches the value calculated in the attempt.

In conclusion, the work done by the piston is 75.01J and the displacement of the piston is 0.015m. These values are consistent with the given information and the calculations are correct. It is important to note that this is a simplified calculation and there may be other factors that can affect the work and displacement, such as friction and the specific design of the piston and combustion chamber.