If the RMS speed of a gas is 300 m/s at 400 K, what will be the RMS speed at 800

₹0.0

Question: If the RMS speed of a gas is 300 m/s at 400 K, what will be the RMS speed at 800 K?

Options:

Correct Answer: 600 m/s

Solution:

RMS speed is proportional to the square root of temperature. v_rms at 800 K = 300 * sqrt(800/400) = 300 * sqrt(2) = 600 m/s.

If the RMS speed of a gas is 300 m/s at 400 K, what will be the RMS speed at 800 K?

If the RMS speed of a gas is 300 m/s at 400 K, what will be the RMS speed at 800 K?

Step 1: Understand that RMS speed (v_rms) is related to temperature (T) by the formula v_rms ∝ √T.
Step 2: Identify the initial RMS speed, which is 300 m/s at an initial temperature of 400 K.
Step 3: Identify the new temperature, which is 800 K.
Step 4: Set up the ratio of the new temperature to the old temperature: 800 K / 400 K = 2.
Step 5: Take the square root of the ratio: √(800/400) = √2.
Step 6: Multiply the initial RMS speed by the square root of the ratio: 300 m/s * √2.
Step 7: Calculate the final RMS speed: 300 m/s * 1.414 (approximate value of √2) = 600 m/s.

RMS Speed and Temperature Relationship – The root mean square (RMS) speed of a gas is directly proportional to the square root of its absolute temperature, which is a key concept in kinetic theory.