Helium gas is in a cylinder that has rigid walls. If the pressure of the gas is 2.00 atm, then the root-mean-square speed of the helium atoms is vrms = 176 m/s. By how much (in atmospheres) must the pressure be increased to increase the vrms of the He atoms by 100 m/s? Ignore any change in the volume of the cylinder

Explanation:

First step

To calculate by how much the pressure has been increased we must find a relation between Vrms and the pressure p

Where M is molar mass,R is gas constant and T is temperature

As R and M is constant so we obtain

Vrams∝√T

Second step

From Ideal gas law we know that

we will find that

p∝T

So from first and second step, we can obtain that

Vrms∝√p

And a relation between both of them could be given by:

The pressure is increased to 4.1988 atm, so the amount will be given by:

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