Equations of perfect gases.
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Equations of perfect gases.
I have a few questions regarding the simple equations of perfect gases but I just can't make sense from them. They're the following:
1. At a constant pressure, the volume of a gas is proportional to the temperature and density.
2. At constant volume, the pressure of a gas is proportional to the temperature and inversely proportional to the density.
3. At constant temperature, the volume of a gas is inversely proportional to the pressure but directly proportional to the density.
I understand the relationships between pressure, volume and temperature (PV/T=constant) but not with how they relate to density.
Could someone briefly explain the three main points?
Thanks.
1. At a constant pressure, the volume of a gas is proportional to the temperature and density.
2. At constant volume, the pressure of a gas is proportional to the temperature and inversely proportional to the density.
3. At constant temperature, the volume of a gas is inversely proportional to the pressure but directly proportional to the density.
I understand the relationships between pressure, volume and temperature (PV/T=constant) but not with how they relate to density.
Could someone briefly explain the three main points?
Thanks.
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Think of it this way: the pressure a gas exerts on its container is due to collisions between gas molecules and the container walls. The temperature governs how hard they hit, and the density is how many molecules there are within the space.
If there's a very low density in a given volume but a high temperature, then the molecules will be hitting the walls with plenty of energy, but not very often, so we'll see a some pressure. Alternatively, we can have lots of molecules (high density), but with low energy. We'll still have the same pressure, because although they're not moving as quickly they're hitting the walls more frequently.
If we want a higher pressure, we need the few gas molecules to hit the walls more often, so we need to move the walls closer together... ie, make the volume smaller, or put more molecules in there (increase the density).
Hope this helps,
David.
If there's a very low density in a given volume but a high temperature, then the molecules will be hitting the walls with plenty of energy, but not very often, so we'll see a some pressure. Alternatively, we can have lots of molecules (high density), but with low energy. We'll still have the same pressure, because although they're not moving as quickly they're hitting the walls more frequently.
If we want a higher pressure, we need the few gas molecules to hit the walls more often, so we need to move the walls closer together... ie, make the volume smaller, or put more molecules in there (increase the density).
Hope this helps,
David.
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The general noble gas equation is
PV = nRT
where P=Pressure, V=Volume, n=number of molecules, R=a gas constant, and T=Temperature.
It can be reduced to
PV/T = a constant
for a closed system. That means that if any of the variables are changed, one or both of the others must change to compensate.
PV = nRT
where P=Pressure, V=Volume, n=number of molecules, R=a gas constant, and T=Temperature.
It can be reduced to
PV/T = a constant
for a closed system. That means that if any of the variables are changed, one or both of the others must change to compensate.
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As Intruder alludes to perhaps the reason you are not making the connection is because of the equation you are using. I.E PV/T=Constant..
There are different ways to express the Ideal gas equation.. one way is using an individual gas constant.. I.E PV=mRT (the mR bit would be your constant) m= mass and R= individual gas constant.. the best thing about this form of the equation is that it can easily modified to calculate density. Density is mass per unit volume or p=m/V (where p=density). If you do a bit of rearranging of the first equation so P=mRT/V then substitute m/V for p you end up with the equation P=pRT. I.E.
A tank with a volume of 1m^3 is filled with air (individual gas constant R=287.05) compressed to a gauge pressure of 0 psi (atmospheric pressure of 14.696 psi (101.325 kpa). The temperature in the tank is 20c (293.15k). Find the density...
p=P/RT
p= (14.696 psi)(6894.75 Pa)/(20+273.15)(287.05)
p=1.20 kg/m^3
I suggest you use S.I units.. Kilograms for mass, Kelvin for Temperature, Pascals for Pressure Meters^3 for volume and Kg/m^3 for density. You could also use Imperial units as long as you don't mix the two together in the equations it will still work ..
I hope this is of some help ?
There are different ways to express the Ideal gas equation.. one way is using an individual gas constant.. I.E PV=mRT (the mR bit would be your constant) m= mass and R= individual gas constant.. the best thing about this form of the equation is that it can easily modified to calculate density. Density is mass per unit volume or p=m/V (where p=density). If you do a bit of rearranging of the first equation so P=mRT/V then substitute m/V for p you end up with the equation P=pRT. I.E.
A tank with a volume of 1m^3 is filled with air (individual gas constant R=287.05) compressed to a gauge pressure of 0 psi (atmospheric pressure of 14.696 psi (101.325 kpa). The temperature in the tank is 20c (293.15k). Find the density...
p=P/RT
p= (14.696 psi)(6894.75 Pa)/(20+273.15)(287.05)
p=1.20 kg/m^3
I suggest you use S.I units.. Kilograms for mass, Kelvin for Temperature, Pascals for Pressure Meters^3 for volume and Kg/m^3 for density. You could also use Imperial units as long as you don't mix the two together in the equations it will still work ..
I hope this is of some help ?
And Ideal gas laws are most useful at high temperature and low pressure.
If not corrections have to be made, but all of the equations use the form PV=nR{something here involving Temp--- as there are many [like 25] real gas equations}---
the 'something there' are corrective coefficients for intermolecular attractions and repulsions
Popular ones are Van Der Waals, Dietricci's expansions, and the Virial equation of state.
all of which can be rearranged to get to density, but this time under non-ideal conditions high pressure or low temperature----
in atmospheric terms ideal gas laws are very accurate.
If not corrections have to be made, but all of the equations use the form PV=nR{something here involving Temp--- as there are many [like 25] real gas equations}---
the 'something there' are corrective coefficients for intermolecular attractions and repulsions
Popular ones are Van Der Waals, Dietricci's expansions, and the Virial equation of state.
all of which can be rearranged to get to density, but this time under non-ideal conditions high pressure or low temperature----
in atmospheric terms ideal gas laws are very accurate.
