Question

A perfect gas of volume 10 litre is compressed isothermally to a volume of 1 litre. The rms speed of the molecules will

• A. decrease 5 times
• B. remain unchanged
• C. increase 5 times
• D. increase 10 times

Hint:

Always associate "isothermal" directly with "constant temperature" and "constant internal energy". For an ideal gas, if $T$ is constant, average kinetic energy and rms speed must also be constant regardless of pressure or volume changes.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We need to determine how the root mean square (rms) speed of gas molecules changes when the gas is compressed isothermally.

Step 2: Key Formula or Approach:
The rms speed of an ideal gas is strictly dependent on its absolute temperature and molar mass, given by the formula:
$$v_{rms} = \sqrt{\frac{3RT}{M}}$$

Step 3: Detailed Explanation:
The problem explicitly states that the compression is an "isothermal" process.
By definition, an isothermal process is one where the temperature ($T$) of the system remains perfectly constant throughout the volume change.
Since $R$ (universal gas constant) and $M$ (molar mass of the specific gas) are also constants, every term in the formula for $v_{rms}$ remains constant.
The change in volume from 10 litres to 1 litre has no direct effect on the rms speed as long as the temperature is held constant.
Therefore, the rms speed of the molecules remains completely unchanged.

Step 4: Final Answer: The rms speed will remain unchanged, matching option (B).