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Helium gas is in a cylinder that has rigid walls. If the pressure of the gas is 4.00 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. Δp = __________ atm

Question

Helium gas is in a cylinder that has rigid walls. If the pressure of the gas is 4.00 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.

 

Δp = __________ atm

check_circleAnswer
Step 1

Given:

RMS speed of the helium gas at 4 atm pressure = 176 m/s

Step 2

Calculating the new root mean square speed:

3P
Root mean sqaure speed in terms of pressure, vmg
=
(Where P' is the pressure and p is the density of the gas)
If the pressure is 4 atm, Vms
176 m/s
12
(1)
x4
So, 176
After increasing the vms by 100 m/s, the new root mean sqaure speed
(v)s = (176+100) m/s 276 m/s
Let the new pressure be P
3P
.(2)
So, v 276
ms
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3P Root mean sqaure speed in terms of pressure, vmg = (Where P' is the pressure and p is the density of the gas) If the pressure is 4 atm, Vms 176 m/s 12 (1) x4 So, 176 After increasing the vms by 100 m/s, the new root mean sqaure speed (v)s = (176+100) m/s 276 m/s Let the new pressure be P 3P .(2) So, v 276 ms

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Step 3

Calculating the change in pressure to in...

3P
VP
3P
ms
Dividing equation 1 and 2,
(v)
Substitute vmas 176 m/s, (v')ms = 276 m/s and P 4 atm
4
176
276
p 9.84 atm
Hence, the increase in pressure 9.84 atm - 4 atm 5.84 atm
help_outline

Image Transcriptionclose

3P VP 3P ms Dividing equation 1 and 2, (v) Substitute vmas 176 m/s, (v')ms = 276 m/s and P 4 atm 4 176 276 p 9.84 atm Hence, the increase in pressure 9.84 atm - 4 atm 5.84 atm

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Tagged in

Science

Physics

Kinetic Theory of Gases

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