How to Calculate change in volume produced by a piston?

[spacealgae]

Homework Statement

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

Homework Equations

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=??

 

[Bystander]

What do the prefixes mean?

 

[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

 

[SteamKing]

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

Yeah, but what does 'nm' mean?

 

[spacealgae]

Newton-Meter

 

[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.

 

[Mark44]

Yeah, but what does 'nm' mean?

Newton-Meter

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.

 

[Mark44]

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.

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

 

[spacealgae]

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

 

[SteamKing]

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

How many nanometers are in 1 meter?

 

[spacealgae]

1000000000?

 

[SteamKing]

1000000000?

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?

 

[spacealgae]

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

 

[SteamKing]

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

Yes.

 

[Mark44]

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

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

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

Why are you so tentative? Don't you trust your work? Also, be sure to include units.

∆V= Ax∆d

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.

 

[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 !

 

[spacealgae]

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

 

[spacealgae]

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

 

[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?

 

[spacealgae]

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

 

[BvU]

Homework Statement

.. It asks me to calculate the change in volume produced by the piston, and it gives me the equation:
∆V= Ax∆d

Instead of spraying this thread with shots, why not provide the complete problem statement with all variables and given/known data ?
I'm afraid that, because of your subsequent posts, I start to suspect the values for A and $\ \Delta d \$you mention .

 

[spacealgae]

sorry, I just actually figured it out (I think) and got excited. But here we go from the top:
How do I calculate the change in the volume produced by the piston?
Given formula:
∆V=∆x∆d
What I know: distance =1700nm
Area of piston=1x10^-16m^2
What I think I figured out, through the help of this forum, (thank you everyone by the way) was to covert 1700nm into scientific notation, which is 1.7x10^3.
I multiplied 1.7x10^3 with the area of the piston, 1x10^-16m^2, and got the answer 1.7x10^13m^2.
Now, my next question is how to calculate the work done by the gas molecules.
Given formula: W=Px∆V
What I know: Volume=1.7x10^13m^2
A t m (atmospheric pressure)=0.25 A t m

 

[SteamKing]

sorry, I just actually figured it out (I think) and got excited. But here we go from the top:
How do I calculate the change in the volume produced by the piston?
Given formula:
∆V=∆x∆d
What I know: distance =1700nm
Area of piston=1x10^-16m^2
What I think I figured out, through the help of this forum, (thank you everyone by the way) was to covert 1700nm into scientific notation, which is 1.7x10^3.

You've missed an important distinction here. 1 nm = 10 ^-9 m. It's not enough to write 1700 in scientific notation if you lose the nm in the process.

I multiplied 1.7x10^3 with the area of the piston, 1x10^-16m^2, and got the answer 1.7x10^13m^2.

Aside from the error in the distance traveled, 10 ^-16 ⋅ 10³ ≠ 10¹³

Don't you know how to multiply two numbers in scientific notation?

Now, my next question is how to calculate the work done by the gas molecules.
Given formula: W=Px∆V
What I know: Volume=1.7x10^13m^2
A t m (atmospheric pressure)=0.25 A t m

Let's get the basic geometry of a cylinder and fundamental unit operations clear before we tackle work done.

It's the grade school stuff that needs attention here.

 

[spacealgae]

You've missed an important distinction here. 1 nm = 10 ^-9 m. It's not enough to write 1700 in scientific notation if you lose the nm in the process.

Aside from the error in the distance traveled, 10 ^-16 ⋅ 10³ ≠ 10¹³

Don't you know how to multiply two numbers in scientific notation?

Let's get the basic geometry of a cylinder and fundamental unit operations clear before we tackle work done.

It's the grade school stuff that needs attention here.

Yes, yes, I realized I made a mistake and forgot to convert nm to meters. Physics isn't my strong suit, be patient with me. So, once I convert 1700nm to meters, that would be 1.7x10^-6. So I just need to multiply that to 1x10^-16m^2 to get 1.7x10^-22. I'm confused as to if I would add the m^2 at the end of the answer though.

 

[SteamKing]

Yes, yes, I realized I made a mistake and forgot to convert nm to meters. Physics isn't my strong suit, be patient with me. So, once I convert 1700nm to meters, that would be 1.7x10^-6. So I just need to multiply that to 1x10^-16m^2 to get 1.7x10^-22. I'm confused as to if I would add the m^2 at the end of the answer though.

Since you're multiplying meters by square meters, what units would the answer be in? Remember, you are calculating the change in volume.

 

[spacealgae]

cubic meters?

 

[SteamKing]

cubic meters?

Yes.

 

[spacealgae]

Ok, so the final answer would be 1.7x10^-22m^3?

 

[SteamKing]

Ok, so the final answer would be 1.7x10^-22m^3?

Yes, for the change in volume.

 

[spacealgae]

Awesome! Thank you very much! So now that's all figured out how would I multiply that by the atmospheric pressure, 0.25 A t m? Would I convert the A t m to scientific notation and then multiply?