Please see if I am doing this problem right.

A mixture of gasoline vapor and air is placed in an engine cylinder. The piston has an area of 7.4 X 10^-3 m^2 and is displaced inward by 7.2 X 10^-2 M. If 9.5 X 10^5 Pa of pressure is placed on the piston, how much work is done during this process? Is work being done on or by the gas mixture?

Given: A= 7.4 X 10^-3 m^2 d= 7.2 X 10^-2 m
P= 9.5 X 10^5 PA= 9.5 X 10^5 N/m^2

^^^ is that right???

Unknown: V= ?, W=?

V= Ad
W= PV
V= (7.4 X 10^-3 m^2) (7.2 X 10^-2 m) = 5.3 x 10^-4 m^3
W= (9.5 X 10^5 N/m^2) (5.4 X 10^-4 m^3)= 513 J.
W done by the gas= 513 J.

Is any of this right at all or am I completely doing this wrong?
also, how do i figure out if work is being done on or by the gas mixture?

-506.2 J

Yes, that is correct. The negative sign indicates that work is being done on the gas mixture by the piston.

Well, don't worry, you're doing just fine! Your calculations seem to be correct. The volume (V) calculation and the work (W) calculation both look good.

To figure out if work is being done on or by the gas mixture, you can look at the signs. If the work is positive, it means work is being done on the gas. If the work is negative, it means work is being done by the gas.

In this case, the work (W) is positive, so it means work is being done on the gas mixture. So, you got that part right too!

Keep up the good work, and don't be afraid to ask if you have any more questions!

It looks like you have made a couple of errors in your calculations, but overall you are on the right track.

To find the volume (V) of the gas, you correctly used the formula V = Ad, where A is the area of the piston and d is the displacement. However, when you multiplied 7.4 x 10^-3 m^2 by 7.2 x 10^-2 m, you should have gotten 5.328 x 10^-4 m^3, not 5.4 x 10^-4 m^3.

Next, to calculate the work done (W), you correctly used the formula W = PV, where P is the pressure and V is the volume. However, when you multiplied 9.5 x 10^5 N/m^2 by 5.4 x 10^-4 m^3, you should have gotten 513.6 J, not 513 J.

So the correct answers are:
V = 5.328 x 10^-4 m^3
W = 513.6 J

Now, to determine if work is being done on or by the gas mixture, you need to consider the signs of the values involved. Work done on a system is considered positive, while work done by a system is considered negative.

In this case, the pressure is placed on the piston, causing it to be displaced inward. Since the displacement is in the same direction as the force, the work is being done by the gas mixture. Therefore, the work done (W) is negative (-513.6 J).

To summarize:
V = 5.328 x 10^-4 m^3
W = -513.6 J (work done by the gas mixture)

W=(A)(P)(delta X)

W= (7.40x10^-3)(9.5x10^5)(7.20x10^-2)
W= -506.16J