Advertisements
Advertisements
Question
Consider a mixture of 2 mol of helium and 4 mol of oxygen. Compute the speed of sound in this gas mixture at 300 K.
Advertisements
Solution
Number of molecules of helium = 2
Number of molecules of oxygen = 4
When helium and oxygen are mixed, hence the molecular weight of the mixture of gases is given by
`"M"_"mix" = [("n"_1"M"_1 + "n"_2"M"_2)/("n"_1 + "n"_2)]`
`= [(2 xx 4 + 4 xx 32)/(2 + 4)]`kg/mol
`= (8 + 128)/6`
`= 136/6` kg/mol
= 22.6 × 10-3 kg/mol
In addition, helium is monoatomic,
`"C"_("v"_2) = (2"R")/2`
Oxygen is diatomic `"C"_("v"_1) = (5"R")/2`
∴ For the mixture `("C"_"v")_"mix" = ("n"_1"C"_("v"_1) + "n"_2"C"_("v"_2))/("n"_1 + "n"_2)`
`("C"_"v")_"mix" = (2 xx 3/2 "R" + 4 xx 5/2 "R")/(2 + 4) = (13 "R")/6`
From Meyor's relation
`("C"_"p")_"mix" = ("C"_"v")_"mix" + "R"`
`("C"_"p")_"mix" = (13"R")/6 + "R" = (13"R" + "5R")/6 = (19"R")/6`
Ratio of specific heat capacitors of a mixture of gases is
`lambda_"mix" = "C"_"p"/"C"_"v" = ((19"R")/6)/((13"R")/6) = 19/13`
According to Laplace, the speed of sound in a gas is
v = `sqrt((lambda "RT")/("M"))`
v = `sqrt(19/13 xx (8.31 xx 300)/(22.6 xx 10^-3))`
`= sqrt(28420.2/17.68 xx 10^4)`
= 4.009 × 102 m/s
= 400.9 m/s
∴ The speed of sound = 400.9 m/s
APPEARS IN
RELATED QUESTIONS
The engine of a train sounds a whistle at frequency v. The frequency heard by a passenger is
Discuss the following case-
Both are in motion
- Source and Observer approach each other
- Source and Observer resides from each other
- Source chases Observer
- Observer chases Source
A ship in a sea sends SONAR waves straight down into the seawater from the bottom of the ship. The signal reflects from the deep bottom bedrock and returns to the ship after 3.5 s. After the ship moves to 100 km it sends another signal which returns back after 2 s. Calculate the depth of the sea in each case and also compute the difference in height between two cases.
A sound source and listener are both stationary and a strong wind is blowing. Is there a Doppler effect?
How do animals sense impending danger of hurricane?
If a star appearing yellow starts accelerating towards the earth, its colour appears to be turned ______.
A source of sound is moving towards a stationary observer with velocity 'Vs' and then moves away with velocity 'Vs'. Assume that the medium through which the sound waves travel is at rest, if 'V' is the velocity of sound and 'n' is the frequency emitted by the source, then the difference between the apparent frequencies heard by the observer is ______.
The period of rotation of the sun at its equator is T and its radius is R. Then the Doppler wavelength shift expected for light with wavelength λ emitted from the edge of the sun's disc is: [c = speed of light]
When an engine passes near to a stationary observer then its apparent frequencies occurs in the ratio 5/3. If the velocity of engine is ______.
When an observer moves towards a stationary source with velocity 'V₁', the apparent frequency of emitted note is 'F₁'. When observer moves away from stationary source with velocity 'V₁' the appearent frequency is 'F2'. If 'v' is velocity of sound in air and \[\frac {F_1}{F_2}\] = 2, then \[\frac {V}{V_1}\] is equal to ______.
