Answer
Verified
39.6k+ views
Hint: The given question is from kinetic theory of gases and speed of sound in gaseous medium. As we know that velocity of sound depends on adiabatic constant, pressure of gas and molecular mass of gas in a specific relation. So we use this relation to solve this problem.
Complete step by step answer:
According to kinetic theory of gases the speed of sound in a gas medium depends on many factors like atomicity of gas, pressure of gas and molecular weight of gas molecules. This relation of speed of sound is given by
$v = \sqrt {\dfrac{{\gamma P}}{\rho }} $$ = \sqrt {\dfrac{{\gamma RT}}{M}} $
Where $v$= speed of sound
$\gamma $= Adiabatic constant for gas
$P$= Pressure of gas
$\rho $= density of gas
R= Universal gas constant
T= Temperature of gas
M= Molecular weight of gas
The given parameters in above question are
Hydrogen$ \Rightarrow {M_{{H_2}}} = 2$
Oxygen$ \Rightarrow {M_{{O_2}}} = 32$
Temperature is the same for both gases as per given condition. And both gases have the same atomicity so the value of adiabatic constant will also be the same.
So from the above mentioned formula we can say that $\gamma RT$ will have constant value for both gases and the value of speed of sound will depend only on the molecular mass of gas.
$v \propto \sqrt {\dfrac{1}{M}} $
After comparing both gases, we get
$\dfrac{{{v_{{H_2}}}}}{{{v_{{O_2}}}}} = \sqrt {\dfrac{{{M_{{O_2}}}}}{{{M_{{H_2}}}}}} $
$\dfrac{{{v_{{H_2}}}}}{{{v_{{O_2}}}}} = \sqrt {\dfrac{{32}}{2}} = \dfrac{4}{1}$
So the ratio of speed of sound in hydrogen and oxygen gas will be 4 : 1.
The correct answer is option (B).
Note: Here it is important to note that we have taken the same value of $\gamma$ for both the gases as hydrogen and oxygen exist as diatomic molecules and hence they will have the same degrees of freedom and hence the same $\gamma$.
Complete step by step answer:
According to kinetic theory of gases the speed of sound in a gas medium depends on many factors like atomicity of gas, pressure of gas and molecular weight of gas molecules. This relation of speed of sound is given by
$v = \sqrt {\dfrac{{\gamma P}}{\rho }} $$ = \sqrt {\dfrac{{\gamma RT}}{M}} $
Where $v$= speed of sound
$\gamma $= Adiabatic constant for gas
$P$= Pressure of gas
$\rho $= density of gas
R= Universal gas constant
T= Temperature of gas
M= Molecular weight of gas
The given parameters in above question are
Hydrogen$ \Rightarrow {M_{{H_2}}} = 2$
Oxygen$ \Rightarrow {M_{{O_2}}} = 32$
Temperature is the same for both gases as per given condition. And both gases have the same atomicity so the value of adiabatic constant will also be the same.
So from the above mentioned formula we can say that $\gamma RT$ will have constant value for both gases and the value of speed of sound will depend only on the molecular mass of gas.
$v \propto \sqrt {\dfrac{1}{M}} $
After comparing both gases, we get
$\dfrac{{{v_{{H_2}}}}}{{{v_{{O_2}}}}} = \sqrt {\dfrac{{{M_{{O_2}}}}}{{{M_{{H_2}}}}}} $
$\dfrac{{{v_{{H_2}}}}}{{{v_{{O_2}}}}} = \sqrt {\dfrac{{32}}{2}} = \dfrac{4}{1}$
So the ratio of speed of sound in hydrogen and oxygen gas will be 4 : 1.
The correct answer is option (B).
Note: Here it is important to note that we have taken the same value of $\gamma$ for both the gases as hydrogen and oxygen exist as diatomic molecules and hence they will have the same degrees of freedom and hence the same $\gamma$.
Recently Updated Pages
silver wire has diameter 04mm and resistivity 16 times class 12 physics JEE_Main
A parallel plate capacitor has a capacitance C When class 12 physics JEE_Main
A series combination of n1 capacitors each of value class 12 physics JEE_Main
When propyne is treated with aqueous H2SO4 in presence class 12 chemistry JEE_Main
Which of the following is not true in the case of motion class 12 physics JEE_Main
The length of a potentiometer wire is 10m The distance class 12 physics JEE_MAIN
Other Pages
when an object Is placed at a distance of 60 cm from class 12 physics JEE_Main
A boat takes 2 hours to go 8 km and come back to a class 11 physics JEE_Main
A closed organ pipe and an open organ pipe are tuned class 11 physics JEE_Main
Dissolving 120g of urea molwt60 in 1000g of water gave class 11 chemistry JEE_Main
Explain the construction and working of a GeigerMuller class 12 physics JEE_Main
If a wire of resistance R is stretched to double of class 12 physics JEE_Main