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Chapter 3: Q66P (page 614)

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

Short Answer

Expert verified

The pressure is increased by to increase of He atom by .

Step by step solution

01

Determine the Formula for  and relation between  and pressure

The root mean square velocity is express by

................equation 1

The relation between Root mean square velocity and pressure is

The rms depends only on temperature ,

Thus use ideal gas equation ,

hence , ,

......................equation 2

02

Determine increase in pressure to increase of He atom by

Helium gas is at

Then pressure increase to

Then ,

Solve for pressure by using equation 2

The pressure is increased to ,So the amount of increase is

Therefore , the pressure is increased by to increase of He atom by .

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