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Thermodynamics total kinetic energy and rms velocity 
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#1
May2811, 04:55 PM

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Find total kinetic energy and root mean square velocity of the molecules of 10 liters of helium gas at an equilibrium pressure of 105 N m−2. Density of helium is 0.1786 gram/liter.
I am having trouble with the question, I know: K=(Nm<v^2>)/2 PV=(Nm <v^2>)/3 but I am not sure how to apply this. Any help would be appreciated. 


#2
May2811, 06:22 PM

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#3
May2911, 02:42 AM

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I have partial solutions from my tutorial but they are not making too much sense...
From the above equations, it goes: K= 1/2 Nm <v>^2 so if divide each side by V K= 1/2 ρ V <v>^2 from here the solution goes: PV=1/3 Nm <v>^2 K=3/2 PV I can see that 2K=3PV but i do not understand where the following equations come from: K=1/3 ρ V <v>^2 because this is what i need to rearrange to find Vrms. 


#4
May2911, 06:16 AM

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Thermodynamics total kinetic energy and rms velocity
You did not answer my questions.
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#5
May2911, 06:44 AM

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I know that as the temp increases so does the kinetic energy.
1/2 m <v>^2 = 3/2 KT 


#6
May2911, 10:22 AM

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#7
Jul1311, 08:58 PM

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I'm not sure if you still need help with this question, but I'll show how I'd work it out:
Firstly, to find the RMS (root mean squared) velocity of the molecules, we'll start with your equation, PV=(Nm <v^2>)/3 Now we don't know N, and while we could calculate it, its easier to rearrange this equation to form, P = (Nm<v^2>)/3V (multiplying both sides by V) P = (1/3)p<v^2> (using Nm/V = p (density) ) Now we know p the density, and P the pressure so rearrange <v^2> = 3P/p <v^2> = 3 x 105 / (0.1786 x 10^3 / 10^3 ) [ensuring p is in kg/m^3] <v^2> = 1763.7178... RMS = 42.0 ms^1 (3sf) [square root the <v^2>] Secondly to find the total Kinetic energy Start with what we have, so P = Nm<v^2> / 3V and K= 1/2 Nm <v^2> So 3PV = Nm<v^2> 3PV/2 = 1/2 Nm<v^2> and since K = 1/2 Nm<v^2> We can state that K = 3/2 PV and can now substitute your values in to find the answer. There are many ways of solving these as they are all rearrangements of the same equation. 


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