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  • Figure shows a parabolic graph between <img alt="\mathrm{T \: and \: \frac{1}{V}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7BT%20%5C%3A%20and%20%5C%3A%20%5Cfrac%7B1%7D%7BV%7D

Figure shows a parabolic graph between \mathrm{T \: and \: \frac{1}{V}} for a mixture of a gas undergoing an adiabatic process. What is the ratio of \mathrm{v_{r m s}} and speed of sound in the mixture?


 

Option: 1

\mathrm{\sqrt{\frac{3}{2}}}

 


Option: 2

\sqrt{2}
 


Option: 3

\sqrt{\frac{2}{3}}
 


Option: 4

\sqrt{3}


Answers (1)

best_answer

Equation of the parabola given in the graph is

\mathrm{ \mathrm{y}^2=4 \mathrm{ax} }

\mathrm{ \left(T_o\right)^2=4 a\left(\frac{1}{V_o}\right) }

\mathrm{\Rightarrow \quad T_o^2 V_o=\text { constant } }

\mathrm{ T_o V_o^{1 / 2}=\text { constant } \quad \text { [for an adiabatic process } \mathrm{TV}^{\gamma-1}=\text { constant] } }

\mathrm{\therefore \quad \gamma-1=1 / 2 \Rightarrow \gamma=3 / 2}

\mathrm{\frac{v_{\text {rms }}}{v_{\text {sound }}}=\frac{\sqrt{\left(\frac{3 R T}{M}\right)}}{\sqrt{\frac{\gamma R T}{M}}}=\sqrt{\frac{3}{\gamma}}=\sqrt{2}}

\therefore option 2 is correct.






 

Posted by

Riya

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