Question

The temperature of an ideal gas is increased from 27°C to 127°C, then the percentage increase in \( v_{\text{rms}} \) is

• A. 37%
• B. 11%
• C. 33%
• D. 15.5%

Hint:

The root mean square velocity of an ideal gas is directly proportional to the square root of the temperature.

Answer 1

The Correct Option is D

Step 1: Use the formula for the root mean square velocity.
The \( v_{\text{rms}} \) is related to the temperature by \( v_{\text{rms}} = \sqrt{\frac{3kT}{m}} \). The temperature is in Kelvin, so we first convert the temperatures: - Initial temperature = \( 27°C = 300 \, \text{K} \) - Final temperature = \( 127°C = 400 \, \text{K} \)
Step 2: Calculate the percentage increase.
The percentage increase in \( v_{\text{rms}} \) is given by: \[ \frac{v_{\text{rms, final}} - v_{\text{rms, initial}}}{v_{\text{rms, initial}}} \times 100 = 15.5\% \] Final Answer: \[ \boxed{15.5\%} \]