Help with rms speed of gas when molecules are doubled

AI Thread Summary
In a constant volume container with constant pressure, doubling the number of gas molecules affects the root mean square (rms) speed. The initial rms speed is given as 1300 m/s, but without the initial temperature or the mass of the gas, the final rms speed cannot be directly calculated. However, since pressure is constant and the number of molecules is doubled, the temperature must decrease to maintain this condition. The relationship between temperature and rms speed indicates that if temperature decreases, the final rms speed will also decrease. Understanding these relationships is crucial for solving the problem accurately.
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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