Question

The temperature at which the r.m.s. velocity of a gas triples to its r.m.s. velocity at \(0^\circ\text{C}\) is

• A. \(2184\,\text{K}\)
• B. \(2184^\circ\text{C}\)
• C. \(2100^\circ\text{C}\)
• D. \(2100\,\text{K}\)

Hint:

The r.m.s. speed of a gas varies as the square root of absolute temperature: \[ v_{\text{rms}}\propto \sqrt{T}. \] Always convert Celsius temperature into Kelvin before using this relation.

Answer 1

The Correct Option is B

Step 1: Relate r.m.s. speed to absolute temperature.
v_rms ∝ √T. For tripling: 3 = √(T₂/T₁).

Step 2: Solve for final temperature.
T₁ = 273 K. 9 = T₂/273 → T₂ = 2457 K.

Step 3: Convert to Celsius.
T₂ = 2457 – 273 = 2184°C.

Step 4: Final Answer:
2184°C.