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Chapter 19: Q28P (page 578)

Question: At what frequency would the wavelength of sound in air be equal to the mean free path of oxygen molecules at 1 atmpressure and 0.00 0C? The molecular diameter is3.0脳10-8cm.

Short Answer

Expert verified

Answer

The required value of frequency is3.5脳109Hz .

Step by step solution

01

Given data

  • Temperature;

T=0.00掳C=273.15K

  • Pressure;

p=1.0atm=1.01脳105Pa

  • Molecular diameter;

d=3.0脳10-8cm=3.0脳10-10m

02

Understanding the concept

The expression for the velocity of sound is given by,

v=f位

Here v is the velocity of the sound, F is the frequency,位 is the wavelength.

03

Calculate the frequency at which wavelength of sound in air would be equal to the mean free path of oxygen molecules at 1 atm pressure and 0.00 0C

L=位

From the above expression,

,v=f位

Substitute for into the above equation,

f=331位

Let the mean free path of oxygen molecules be L ,

Given condition is

L=位

Hence,

f=331L

But,L=12蟺d2NV

Also, according to the gas law,

NV=pkT

Therefore,

f=33112蟺d2pkT

Substitute 3.0脳10-10mfor d , 1.01脳105Pa for p , 1.38脳10-23鈥�J/molecule鈥�路Kfor k and273.15鈥�K for T into the above equation.

f=331123.142(3.0脳10-10)21.01脳1051.38脳10-23273.15=3.54脳109鈮�3.5脳109Hz

Therefore, the required value of frequency is3.5脳109Hz .

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Most popular questions from this chapter

Question: Find the rms speed of argon atoms at 313 K.Molar mass of argon atoms is 39.948 g/ mol.

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Question: From the knowledge that Cv , the molar specific heat at constant volume, for a gas in a container is 5.0 R , calculate the ratio of the speed of sound in that gas to the rms speed of the molecules, for gas temperature T. (Hint: See Problem 91.)

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