MHT CET · Physics · Kinetic Theory of Gases
At what temperature rms speed of air molecules is doubled of that at NIP ?
- A \(819^{\circ} \mathrm{C}\)
- B \(719^{\circ} \mathrm{C}\)
- C \(909^{\circ} \mathrm{C}\)
- D None of these
Answer & Solution
Correct Answer
(A) \(819^{\circ} \mathrm{C}\)
Step-by-step Solution
Detailed explanation
\(
v_{\mathrm{rms}} \propto \sqrt{T}
\)
\(
\begin{aligned}
\Rightarrow & \frac{v_{1}^{2}}{v_{2}^{2}}=\frac{T_{1}}{T_{2}} \\
\Rightarrow & \frac{v^{2}}{4 v^{2}} =\frac{273}{T_{2}} \\
\Rightarrow & T_{2} =1092 \mathrm{~K} \\
&=819{ }^{\circ} \mathrm{C}
\end{aligned}
\)
v_{\mathrm{rms}} \propto \sqrt{T}
\)
\(
\begin{aligned}
\Rightarrow & \frac{v_{1}^{2}}{v_{2}^{2}}=\frac{T_{1}}{T_{2}} \\
\Rightarrow & \frac{v^{2}}{4 v^{2}} =\frac{273}{T_{2}} \\
\Rightarrow & T_{2} =1092 \mathrm{~K} \\
&=819{ }^{\circ} \mathrm{C}
\end{aligned}
\)
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