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April 30th, 2017, 09:24 PM   #1
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Solve For Pressure Applied

The volume V of a gas varies inversely as the pressure P on it. If the volume is 250 cm$\displaystyle ^3$ under a pressure of 35 kg/cm$\displaystyle ^3$, solve for the pressure applied to have a volume of 180 cm$\displaystyle ^3$. Be sure to define your variables, find your constant variable, construct your variation equation, and then solve.
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May 2nd, 2017, 02:23 AM   #2
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The question states the steps you need to take to solve it.

1. Define your variables
2. Find your constant variable
3. Construct your variation equation
4. Solve it

The question also hints at the things that are going to be variables in your equation, volume and pressure, and how they are related to each other.

Therefore, have a go and let us know how it goes
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May 3rd, 2017, 08:05 PM   #3
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V= 250 cm$\displaystyle ^3$ when P=35 kg/cm$\displaystyle ^3$

Correct me if I'm wrong, but since the volume depends on the pressure applied, the constant variable would be V=250cm$\displaystyle ^3$, right?

So:

y=250cm$\displaystyle ^3$

y=kx

when p=35 kg/cm$\displaystyle ^3$, v=250cm$\displaystyle ^3$

35kg/cm$\displaystyle ^3$=k*250cm$\displaystyle ^3$

So the equation would be 35kg/cm$\displaystyle ^3$=250cm$\displaystyle ^3$*x. Am I at all on the right track here?
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May 4th, 2017, 03:10 AM   #4
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Quote:
Originally Posted by Indigo28 View Post
V= 250 cm$\displaystyle ^3$ when P=35 kg/cm$\displaystyle ^3$

Correct me if I'm wrong, but since the volume depends on the pressure applied, the constant variable would be V=250cm$\displaystyle ^3$, right?
Nope, the volume variable, V, varies with the pressure variable, P, so if you change the pressure, you change the volume...


Here's some further information that might help:

There are different names for different quantities in equations depending on their behaviour.

- Variables:
These are quantities that can change and are usually things that describe the state of a system at a particular point in time.

- Independent variables:
These are particular variables that do not depend on anything. Usually they are things like space and time, which you characterise everything else in terms of. Most calculations are decribed as 1D, 2D, 3D, etc. based on the number of independent variables used (hence some people describing 4D as referring to 3 space variables and 1 time variable).

- Dependent variables:
These are particular variables which have dependencies on other things. They have relationships between each other which describe how they vary. The relationships can be described using proportionalities or functions/formulae.

- Constant:
These are quantities that do not change. Therefore, they usually describe the system as a whole or how its processes are working. Variables that just happen to stay the same for some sort of process are sometimes called constants.

- Parameters:
These are constants that are required to solve something at the beginning of a calculation. They are often called input parameters.


Now some information on relationships between variables. Consider two variables, $\displaystyle a$ and $\displaystyle b$...

- Proportional
This means that if you increase one thing, you increase the other (so if you double one quantity, you double the other). Written down, this is

$\displaystyle a \propto b$

where the $\displaystyle \propto$ symbol just means "proportional to". You can turn any proportionality into an equation by multiplying the right-hand side by a constant (most people use k) and swapping the $\displaystyle \propto$ with an equals sign. So you end up with

$\displaystyle a = kb$

If you plot $\displaystyle a$ as a function of $\displaystyle b$ you get a straight line on a plot going through the origin, so this relationship is often called a "linear relationship".

- Inversely proportional
This means that if you increase one thing, you decrease the other (so if you double one quantity, you halve the other). Written down, this is

$\displaystyle a \propto \frac{1}{b}$

Making an equation from this looks like

$\displaystyle a = \frac{k}{b}$



Now onto your gas problem...

In the question there is a statement: "volume of a gas varies inversely as the pressure". That means that both the volume and the pressure are variables and the relationship between those two variables is inverse proportionality (i.e. you halve one thing, you double the other). Written down, this looks like

$\displaystyle V \propto \frac{1}{P}$


Turning this into an equation gives

$\displaystyle V = \frac{k}{P}$

where k is the constant.

You can then substitute the initial volume and pressure parameters to find k. Once you have k, you can use that together with the target volume to get the pressure required.
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Last edited by Benit13; May 4th, 2017 at 03:15 AM.
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