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In an ideal monoatomic gas, the speed of sound is given by 
. If the speed of sound in argon at 25°C us 1245 km h–1, the root mean square velocity in ms–1 is…………….
. If the speed of sound in argon at 25°C us 1245 km h–1, the root mean square velocity in ms–1 is…………….Correct answer is '463'. Can you explain this answer?
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In an ideal monoatomic gas, the speed of sound is given by. If the spe...
From kinetic theory of ideal gas,
vs= sqrt[ 5RT/3M]
But,M=mxNo, where m is mass of Argon atom and No is Avogadro number.
Also, R= kNo, where k is Boltzmann constant. Therefore ,
vs=sqrt[ 5 No kT/3mNo]=sqrt[5kT/3m]……(1)
But, (1/2)m<v2 > =(3/2)kT OR
kT=m<v2>/3. Using this in equation (1),
vs= sqrt[5m<v2>/9m]= sqrt[(5/9)<v2] OR
Sqrt(<v2>)=vs x sqrt(9/5)=1245x(5/18)xsqrt(9/5) OR
v rms= 463.9 m/s.
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In an ideal monoatomic gas, the speed of sound is given by. If the spe...
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In an ideal monoatomic gas, the speed of sound is given by. If the spe...
First we change the speed of sound in meter per second by multiplying it by5/18which would be equal to 345.83m/s.Now put the given speed equal to 345.833
(5RT/M)^1/2= 345.833
(5^1/2)/3 *(3RT/M)^1 /2
345.833=2.24/3(Vrms)
Vrms=(345.833*3)/2.24=463m/s
(5RT/M)^1/2= 345.833
(5^1/2)/3 *(3RT/M)^1 /2
345.833=2.24/3(Vrms)
Vrms=(345.833*3)/2.24=463m/s
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