Effect of density on rms speed in ideal gas eqn

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Homework Help Overview

The discussion revolves around the relationship between density and root mean square (rms) speed in the context of the ideal gas equation, particularly focusing on how these variables interact under conditions of constant temperature.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the implications of the ideal gas equations, particularly questioning how density relates to rms speed when temperature is held constant. There is an attempt to reconcile conflicting interpretations of the equations.

Discussion Status

Some participants have identified a misunderstanding regarding the conditions of the problem, clarifying that the question specifies constant temperature rather than constant pressure. This has led to a re-evaluation of the initial assumptions about the relationship between density and rms speed.

Contextual Notes

There is an ongoing discussion about the implications of the equations provided, particularly regarding the role of density in the context of kinetic energy and rms speed, with some participants questioning the relevance of density in the derived relationships.

toforfiltum
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Homework Statement


upload_2016-4-2_18-24-3.png

upload_2016-4-2_18-24-33.png


Homework Equations


1) PV = nRT
2 )## P = ⅓ ρ<c^2> ##
3) KE ∝ T

The Attempt at a Solution


According to the second equation above, density is inversely proportional to root mean square speed at constant pressure, but the answer states that the root mean square speed depends only on the temperature so the answer is no effect.

I don't see how when the second equation suggests otherwise. Can someone help me out?
 
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toforfiltum said:
According to the second equation above, density is inversely proportional to root mean square speed at constant pressure
Yes, but the question states constant temperature, not constant pressure.
 
haruspex said:
Yes, but the question states constant temperature, not constant pressure.
Oops, how could I misread that. Thanks.
So to prove this, it is ## \frac {1} {2} Nm<c^2> = \frac{3} {2} NkT ## ? Which is KE ∝ T?
Since ρ is not in the above equation, it is proven that density has no effect on root mean square speed?

Thanks!
 
toforfiltum said:
Oops, how could I misread that. Thanks.
So to prove this, it is ## \frac {1} {2} Nm<c^2> = \frac{3} {2} NkT ## ? Which is KE ∝ T?
Since ρ is not in the above equation, it is proven that density has no effect on root mean square speed?

Thanks!
Ok.
 

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