An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas in $n$. The internal energy of one mole of the gas is $U_n$ and the speed of sound in the gas is $v_n$. At a fixed temperature and pressure, which of the following is the correct option?
IIT 2023, Medium
Download our app for free and get started
$\mathrm{U}=\frac{1}{2} \mathrm{fnr} \mathrm{T}=\frac{\mathrm{frT}}{2}$
$\therefore \text { A and } B \text { are wrong. }$
$\mathrm{v}_{\text {sound }}=\sqrt{\frac{\gamma \mathrm{RT}}{\mathrm{M}}}=\sqrt{\left(\frac{2}{\mathrm{f}}+1\right) \frac{\mathrm{RT}}{\mathrm{M}}}$
$\Rightarrow \text { more 'f', less 'v' }$
$\therefore \mathrm{v}_5>\mathrm{v}_7$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1When the temperature of an ideal gas is increased by $600 K$, the velocity of sound in the gas becomes $\sqrt 3 $ times the initial velocity in it. The initial temperature of the gas is .... $^oC$View Solution
- 2A tuning fork $A$ of frequency $200 Hz$ is sounded with fork $B,$ the number of beats per second is $5.$ By putting some wax on $A,$ the number of beats increases to $8.$ The frequency of fork $B$ is .... $Hz$View Solution
- 3A police car horn emits a sound at a frequency $240 Hz$ when the car is at rest. If the speed of the sound is $330 m/s$, the frequency heard by an observer who is approaching the car at a speed of $11 m/s,$ is ... $Hz$View Solution
- 4Two sound waves having a phase difference of $60°$ have path difference ofView Solution
- 5A block of mass $1\,\, kg$ is hanging vertically from a string of length $1\,\, m$ and mass /length $= 0.001\,\, Kg/m$. A small pulse is generated at its lower end. The pulse reaches the top end in approximately .... $\sec$View Solution
- 6What is minimum length of a tube, open at both ends, that resonates with tuning fork of frequency $350 Hz$ ? [velocity of sound in air $= 350 m/s$] ..... $cm$View Solution
- 7A standing wave in a pipe with a length $L=1.2 \,m$ is described by $y(x, t)=y_0 \sin [(2 \pi / L) x] \sin [(2 \pi / L) x+\pi / 4]$ based on above information, which one of the following statement is incorrect? (Speed of sound in air is $300 \,ms ^{-1}$ )View Solution
- 8Two waves are represented by ${y_1} = a\sin \left( {\omega \,t + \frac{\pi }{6}} \right)$ and ${y_2} = a\cos \omega \,t$. What will be their resultant amplitudeView Solution
- 9The length of the wire shown in figure between the pulleys is $1.5\, m$ and its mass is $12.0\,g$. The frequency of vibration with which the wire vibrates in three loops forming antinode at the mid point of the wire is $(g = 9.8 \,m/s^2)$View Solution
- 10An organ pipe is closed at one end has fundamental frequency of $1500 Hz$. The maximum number of overtones generated by this pipe which a normal person can hear is :View Solution