What Temperature Triples the RMS Speed of an Ideal Gas?

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To determine the temperature at which the RMS speed of an ideal gas triples from its initial value at 288K, one must understand the relationship between RMS speed and temperature. The relevant equation is derived from the ideal gas law, indicating that RMS speed is proportional to the square root of temperature. By manipulating the equations, it can be shown that if the RMS speed is tripled, the temperature must increase by a factor of nine. Thus, the new temperature required to achieve this condition is 2592K. Understanding these relationships is crucial for solving similar problems in thermodynamics.
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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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