# How to Calculate change in volume produced by a piston?

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1. Jan 5, 2016

### spacealgae

1. The problem statement, all variables and given/known data
Hello all! I need a little bit of help with my physics homework! It asks me to calculate the change in volume produced by the piston, and it gives me the equation:
∆V= Ax∆d

2. Relevant equations

3. The attempt at a solution
Now I know that A= 1x 10-^16m^2
And ∆d=1700nm
My only problem is that I'm confused on how to calculate the answer with the two given variables! Help!
∆V=1x10-^16m^2x1700nm=??

Last edited by a moderator: Jan 5, 2016
2. Jan 5, 2016

### Bystander

What do the prefixes mean?

3. Jan 5, 2016

### spacealgae

Oh sorry, it means to the 'power of', so to break it down, I believe the variable is:
1 times 10 to the power of -16 m to the power of 2

4. Jan 5, 2016

### SteamKing

Staff Emeritus
Yeah, but what does 'nm' mean?

5. Jan 5, 2016

Newton-Meter

6. Jan 5, 2016

### spacealgae

1. A unit of the meter-kilogram-second system equal to the energy expended, or work done, by a force of one newton acting through a distance of one meter and equal to one joule.

7. Jan 5, 2016

### Staff: Mentor

I don't think so, in the context of this problem. Here it means "nanometer" I believe, or $10^{-9}$ meter.

One problem that you're having is that your units don't match. The cross-sectional area of your piston is in units of square meters ($m^2$), but the piston's stroke is given in units of nanometers (nm). In your calculation you need to be working in the same units, in powers of meters or of nanometers.

8. Jan 5, 2016

### Staff: Mentor

Not relevant. Volume is in units of $(length)^3$ -- no force involved.

9. Jan 5, 2016

### spacealgae

That's weird, because in my notes, it talks about Newton Meter, not Nanometer. Ok, lets say it is in Nanometer though, how would I go about the calculation then?

10. Jan 5, 2016

### SteamKing

Staff Emeritus
How many nanometers are in 1 meter?

11. Jan 5, 2016

### spacealgae

1000000000?

12. Jan 5, 2016

### SteamKing

Staff Emeritus
It's OK to use scientific notation, so people aren't counting zillions of zeroes.

So, if you have Δd = 1700 nm, how many meters is that?

13. Jan 5, 2016

### spacealgae

Ok, in scientific notion, that would be 1.7e-6?

14. Jan 5, 2016

### SteamKing

Staff Emeritus
Yes.

15. Jan 6, 2016

### Staff: Mentor

Units for newton-meters are usually abbreviated as n-m. The abbreviation for nanometers is just nm, no hyphen.

In any case, since you're calculating volume, all of the units have to be length units -- no forces

Why are you so tentative? Don't you trust your work? Also, be sure to include units.
With expressions such as this one, don't write x to indicate multiplication -- it is too easily confused as being a variable.

Have you finished this problem yet. All you need to do is to multiply the area (A) by the linear distance the piston moves (d). The main difficulty in this problem is converting to the same units.

16. Jan 6, 2016

### BvU

That is a really small piston you have there ! What is it made of ?
The stroke of $1.7 \ 10^{-6}$ m is also really really small !

17. Jan 6, 2016

### spacealgae

Ok, so I would just times 1.7x10^3*1x10^16m^2?

18. Jan 6, 2016

### spacealgae

which would equal 1.87x10^-13m^2?

19. Jan 6, 2016

### spacealgae

• Which leads me to my final question, which is to take the volume I just calculated, and calculate the work done by the gas molecules, and the equation for that is: W=Px*∆V
• and I know that the volume is equal to 1.87x10^-13m^2, and the pressure is 0.25 A t m, so how would I multiply those two together then?

20. Jan 6, 2016

### spacealgae

Wait my mistake, it would be 1.7x10^3*1x10^-16=1.7x10^-13