Help with rms speed of gas when molecules are doubled

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SUMMARY

The discussion focuses on calculating the final root mean square (rms) speed of an ideal gas when the number of molecules is doubled while maintaining constant pressure and volume. Given that the initial rms speed is 1300 m/s, the relationship between temperature and the number of molecules is crucial. The relevant equations are Vrms = sqrt[(3kT)/m] and PV = NkT. When the number of molecules (N) is doubled, the temperature (T) must decrease to keep pressure (P) constant, leading to a final rms speed that can be derived from these principles.

PREREQUISITES
  • Understanding of ideal gas laws
  • Familiarity with root mean square speed calculations
  • Knowledge of thermodynamic principles
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation of the ideal gas law and its implications on temperature and pressure
  • Learn how to manipulate the equation Vrms = sqrt[(3kT)/m] for various scenarios
  • Explore the effects of changing the number of molecules on gas properties
  • Investigate real-world applications of rms speed in thermodynamics
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Students studying thermodynamics, physics enthusiasts, and anyone interested in the behavior of gases under varying conditions.

lbumbalo
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Homework Statement


An ideal gas is kept in a container of constant volume. The pressure of the gas is also kept constant. The number of molecules in the gas is doubled. If the initial rms speed is 1300m/s, what is the final rms speed?


Homework Equations


Vrms=sqrt[(3kT)/m]
PV=NkT


The Attempt at a Solution


I've tried to rework the above equations hoping I would find something but there seem to be too many unknowns. I know that you need to lower the temperature of the gas, but I'm not given the initial temp or the final, and I don't know the initial number of molecules. Thanks
 
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lbumbalo said:

Homework Statement


An ideal gas is kept in a container of constant volume. The pressure of the gas is also kept constant. The number of molecules in the gas is doubled. If the initial rms speed is 1300m/s, what is the final rms speed?


Homework Equations


Vrms=sqrt[(3kT)/m]
PV=NkT


The Attempt at a Solution


I've tried to rework the above equations hoping I would find something but there seem to be too many unknowns. I know that you need to lower the temperature of the gas, but I'm not given the initial temp or the final, and I don't know the initial number of molecules. Thanks
Express the initial T in terms of the other variables. If PV is kept constant and N is doubled, what happens to T?

AM
 

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