## Thermodynamics- total kinetic energy and rms velocity

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.

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 Quote by xxx23 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.
Can you find the temperature? What is the relationship between temperature and kinetic energy?

AM
 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 ^2 so if divide each side by V K= 1/2 ρ V ^2 from here the solution goes: PV=1/3 Nm ^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 ^2 because this is what i need to rearrange to find Vrms.

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## Thermodynamics- total kinetic energy and rms velocity

You did not answer my questions.

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

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 Quote by xxx23 I know that as the temp increases so does the kinetic energy. 1/2 m ^2 = 3/2 KT
You haven't answered my first question: what is the temperature of the Helium? (hint: assume it is an ideal gas).

AM
 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 )/3 Now we don't know N, and while we could calculate it, its easier to rearrange this equation to form, P = (Nm)/3V (multiplying both sides by V) P = (1/3)p (using Nm/V = p (density) ) Now we know p the density, and P the pressure so rearrange = 3P/p = 3 x 105 / (0.1786 x 10^-3 / 10^-3 ) [ensuring p is in kg/m^3] = 1763.7178... RMS = 42.0 ms^-1 (3sf) [square root the ] Secondly to find the total Kinetic energy Start with what we have, so P = Nm / 3V and K= 1/2 Nm So 3PV = Nm 3PV/2 = 1/2 Nm and since K = 1/2 Nm 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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