Q118 / 150 · MHT CET 2026 (18 April Shift 2) · Physics
When the r.m.s. velocity of a gas is denoted by '$v$' at temperature '$T$'. Out of the following relations, the true one is
- A$v \cdot T^2 = \text{constant}$
- B$\dfrac{v}{T^2} = \text{constant}$
- C$v^2 T = \text{constant}$
- Correct answerD$\dfrac{v^2}{T} = \text{constant}$
Solution
The root mean square (r.m.s.) velocity of a gas is given by the expression:
$v = \sqrt{\dfrac{3RT}{M}}$
Squaring both sides, we get:
$v^2 = \dfrac{3RT}{M}$
For a given gas, the molar mass $M$ and the universal gas constant $R$ are constants. Thus:
$v^2 \propto T$
$\dfrac{v^2}{T} = \text{constant}$
Answer: $\dfrac{v^2}{T} = \text{constant}$
$v = \sqrt{\dfrac{3RT}{M}}$
Squaring both sides, we get:
$v^2 = \dfrac{3RT}{M}$
For a given gas, the molar mass $M$ and the universal gas constant $R$ are constants. Thus:
$v^2 \propto T$
$\dfrac{v^2}{T} = \text{constant}$
Answer: $\dfrac{v^2}{T} = \text{constant}$
Hence, the correct answer is option: 'D'.