MHT CET · Physics · Kinetic Theory of Gases
When the rms velocity of a gas is denoted by \(V\), which of the following relation is true? ( \(T=\) absolute temperature of the gas)
- A \(\frac{V^2}{T}=\) constant
- B \(V T^2=\) constant
- C \(\frac{V}{T^2}=\) constant
- D \(V^2 T=\) constant
Answer & Solution
Correct Answer
(A) \(\frac{V^2}{T}=\) constant
Step-by-step Solution
Detailed explanation
RMS velocity is given by
\(\begin{aligned} V & =\sqrt{\frac{3 k T}{m}} \\ V^2 & =\frac{3 k T}{m}\end{aligned}\)
For a gas, \(k\) and \(m\) are constants, so option A is true.
\(\begin{aligned} V & =\sqrt{\frac{3 k T}{m}} \\ V^2 & =\frac{3 k T}{m}\end{aligned}\)
For a gas, \(k\) and \(m\) are constants, so option A is true.
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