NEET · Physics · STD 11 - 12 . kinetic theory of gases
The molecules of a given mass of a gas have \(r.m.s.\) velocity of \(200 \,m s^{-1}\) at \(27^o C\) and \(1.0 \times 10^5 \,Nm^{-2}\) pressure. When the temperature and pressure of the gas are respectively, \(127^o C\) and \(0.05 \times 10^5 \,Nm^{-2},\) the \(r.m.s.\) velocity of its molecules in \(m s^{-1}\) is
- A \(\frac{{400}}{{\sqrt 3 }}\)
- B \(\;\frac{{100\sqrt 2 }}{3}\)
- C \(\;\frac{{100}}{3}\)
- D \(\;100\sqrt 2 \)
Answer & Solution
Correct Answer
(A) \(\frac{{400}}{{\sqrt 3 }}\)
Step-by-step Solution
Detailed explanation
\({\text { As, } v_{\operatorname{ms}}=\sqrt{\frac{3 k_{B} T}{m}}} \) \({\therefore \frac{v_{27}}{v_{127}}=\sqrt{\frac{27+273}{127+273}}=\sqrt{\frac{300}{400}}=\frac{\sqrt{3}}{2}} \)
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