Difference between revisions of "Ideal gas law"
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where <math>R</math> is the [[universal gas constant]]. For [[SI]] units, <cmath>R=8.314 \frac{\text{J}}{\text{mol}\cdot\text{K}}</cmath> | where <math>R</math> is the [[universal gas constant]]. For [[SI]] units, <cmath>R=8.314 \frac{\text{J}}{\text{mol}\cdot\text{K}}</cmath> | ||
| − | As a result, <math> | + | As a result, <math>\frac{PV}{T}=nR</math> thus for any fixed number of moles of gas, the quantity <math>\frac{PV}{T}</math> is constant. |
This equation is relevant to low-[[density]], low-pressure gases. For higher densities, it is necessary to correct this equation. For greater precision, the [[van der Waals equation]] is another equation of state which does apply to higher-pressure gases. | This equation is relevant to low-[[density]], low-pressure gases. For higher densities, it is necessary to correct this equation. For greater precision, the [[van der Waals equation]] is another equation of state which does apply to higher-pressure gases. | ||
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==Problems== | ==Problems== | ||
===Introductory=== | ===Introductory=== | ||
| − | If an ideal gas is in a container of dimensions 1 meter, 1 meter, and 2 meters, at a pressure of 100 kPa, and the container is reduced to 1/8th of its former dimensions while keeping the temperature constant, what will the pressure in the container be after reduction? | + | If an ideal gas is in a container of dimensions 1 [[meter]], 1 meter, and 2 meters, at a pressure of 100 kPa, and the container is reduced to 1/8th of its former dimensions while keeping the temperature [[constant]], what will the pressure in the container be after reduction? |
===Intermediate=== | ===Intermediate=== | ||
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* [[Equation of state]] | * [[Equation of state]] | ||
* [[Thermodynamics]] | * [[Thermodynamics]] | ||
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| + | [[Category:Physics]] | ||
Latest revision as of 08:59, 11 March 2008
The Ideal Gas Law is a law of physics, specifically thermodynamics, which describes the properties of an ideal gas.
The Law
The ideal gas law unifies Boyle's Law and Charles' Law, relating pressure, volume, temperature, and the number of moles of gas. It is thus an equation of state.
It states, for a volume 
containing 
moles of a gas at pressure 
and temperature ,
![\[PV=nRT\]](http://latex.artofproblemsolving.com/a/f/b/afbf75797b7bfc7b97f585bb682af0bacfd0a7d4.png)
where 
is the universal gas constant. For SI units, ![\[R=8.314 \frac{\text{J}}{\text{mol}\cdot\text{K}}\]](http://latex.artofproblemsolving.com/a/d/0/ad05682b6a746dfef8f56b11a6f6dc2a15a58806.png)
As a result, 
thus for any fixed number of moles of gas, the quantity 
is constant.
This equation is relevant to low-density, low-pressure gases. For higher densities, it is necessary to correct this equation. For greater precision, the van der Waals equation is another equation of state which does apply to higher-pressure gases.
Problems
Introductory
If an ideal gas is in a container of dimensions 1 meter, 1 meter, and 2 meters, at a pressure of 100 kPa, and the container is reduced to 1/8th of its former dimensions while keeping the temperature constant, what will the pressure in the container be after reduction?
