What Temperature Triples the RMS Speed of an Ideal Gas?

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SUMMARY

The discussion centers on determining the temperature at which the root mean square (RMS) speed of an ideal gas triples, starting from an initial temperature of 288K. The relevant equations include the ideal gas law, PV = NkbT, and the relationship between pressure and RMS speed, P = (NmV²)/3V. The solution involves equating the two equations to derive T = (mv²)/Kb, highlighting the mathematical relationship between RMS speed and temperature for ideal gases.

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  • Understanding of the ideal gas law (PV = NkbT)
  • Knowledge of root mean square speed (vrms) in kinetic theory
  • Familiarity with the equipartition principle
  • Basic algebra for manipulating equations
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  • Study the derivation of RMS speed for ideal gases
  • Learn about the equipartition theorem in thermodynamics
  • Explore the implications of temperature changes on gas behavior
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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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