Representing pressure of a gas?

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magic_andrew
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#1
Report Thread starter 7 years ago
#1
Show that the pressure of a gas can be represented by P = (p<c>​2)/3
Not sure if those tags were just a formatting error but I've included them just in case.
So far I have used p = m/v and substituted it into the equation PV = 1/3Nmc2rms. So I've got P = 1/3 Npc2rms. Is the N necessary and does the rms part matter?
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lerjj
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#2
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#2
Not that relevant, but in at least some contexts <x> means average value of x. That's probably what the tags meant.
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Stonebridge
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#3
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#3
(Original post by magic_andrew)
Not sure if those tags were just a formatting error but I've included them just in case.
So far I have used p = m/v and substituted it into the equation PV = 1/3Nmc2rms. So I've got P = 1/3 Npc2rms. Is the N necessary and does the rms part matter?
N matters because it's the number of atoms.
If m is the mass of one atom then Nm is the total mass of gas.
Nm/V is density as it's mass / volume.
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Phichi
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#4
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#4
(Original post by magic_andrew)
Not sure if those tags were just a formatting error but I've included them just in case.
So far I have used p = m/v and substituted it into the equation PV = 1/3Nmc2rms. So I've got P = 1/3 Npc2rms. Is the N necessary and does the rms part matter?
&lt;v&gt; represents the mean value.

However:

v_{rms} = \sqrt{&lt;v^2&gt;} \neq \, \, &lt;v&gt;, also, &lt;v^2&gt; \, \,  \neq \, \,  &lt;v&gt;^2

Your question was to prove:

P = (p<c>​2)/3

Are you you positive it wasn't P = \dfrac{1}{3}p&lt;c^2&gt;
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magic_andrew
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#5
Report Thread starter 7 years ago
#5
(Original post by Phichi)
&lt;v&gt; represents the mean value.

However:

v_{rms} = \sqrt{&lt;v^2&gt;} \neq \, \, &lt;v&gt;, also, &lt;v^2&gt; \, \,  \neq \, \,  &lt;v&gt;^2

Your question was to prove:

P = (p<c>​2)/3

Are you you positive it wasn't P = \dfrac{1}{3}p&lt;c^2&gt;
Yeh it's definetly outside the tags. It might just be a mistake by my lecturer so if it helps then just use the power inside the tags.
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Dalek1099
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#6
Report 7 years ago
#6
(Original post by magic_andrew)
Yeh it's definetly outside the tags. It might just be a mistake by my lecturer so if it helps then just use the power inside the tags.
You just need to use pressure=nm/v I am been through this with my lecturer there isn't really much more to the question than that and rearranging the <c^2> is definetley supposed to be (c rms) squared.
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magic_andrew
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#7
Report Thread starter 7 years ago
#7
So the N pretty much acts like a constant and cancel out?
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