What Temperature Triples the RMS Speed of an Ideal Gas?

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Homework Help Overview

The problem involves determining the temperature at which the root mean square (rms) speed of an ideal gas is tripled from its initial value at 288K. The context is rooted in the behavior of ideal gases and their properties related to temperature and speed.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the mathematical relationship between rms speed and temperature, with one participant expressing confusion about the temperature aspect of the problem. Another participant attempts to derive a relationship using the ideal gas equation and considers the implications of pressure and volume.

Discussion Status

The discussion is ongoing, with participants exploring relevant equations and concepts. Some guidance has been offered regarding the mathematical relationships involved, but there is no explicit consensus on the solution or approach yet.

Contextual Notes

Participants are navigating the complexities of the ideal gas laws and the implications of temperature on rms speed, with some assumptions about the relationships between variables being questioned.

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Homework Statement



An ideal gas has rms speed vrms at a temperature of 288K .

At what temperature is the rms speed tripled?

Homework Equations



P=(NmV2)/3V

The Attempt at a Solution




I'm kind of stumped on this one. Other ones I've done are pretty simple to figure out, but the temperature is what is kicking me
 
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What is the mathematical relationship between rms speed and temperature for an ideal gas? That would be a relevant equation here.
 
cepheid said:
What is the mathematical relationship between rms speed and temperature for an ideal gas? That would be a relevant equation here.

Ok so the ideal gas equation is PV=NkbT

Since i see pressure there i divided the volume so i can get P=(NkbT)/v

I set the 2 equations equal to each other and simplified to get T=(mv2)/Kb

if that makes any sense.
 

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