Question

If a gas is compressed isothermally then the r.m.s. velocity of the molecules

• A. remains the same.
• B. increases.
• C. decreases.
• D. first decreases and then increases.

Hint:

For isothermal processes, the temperature remains constant, and thus the r.m.s. velocity of gas molecules does not change.

Answer 1

The Correct Option is A

Step 1: Understanding the r.m.s. velocity and isothermal compression.
The root mean square (r.m.s.) velocity of gas molecules is given by the equation: \[ v_{\text{rms}} = \sqrt{\frac{3kT}{m}} \] where \( k \) is the Boltzmann constant, \( T \) is the temperature, and \( m \) is the molecular mass.
Step 2: Analyzing the effect of isothermal compression.
In an isothermal process, the temperature \( T \) remains constant. Since the r.m.s. velocity depends only on the temperature (and not the pressure or volume directly in an isothermal process), the r.m.s. velocity does not change.
Step 3: Conclusion.
Therefore, the correct answer is (A) because the r.m.s. velocity of gas molecules remains constant during isothermal compression.