Question

An ideal gas is heated at constant volume until its pressure doubles. Which one of the following statements is correct?

• A. The mean speed of the molecules doubles
• B. Root mean square speed of the molecules doubles
• C. Mean square speed of the molecules doubles
• D. Mean square speed of the molecules remains unchanged

Answer 1

Answer: (C)

Mean square speed of the molecules doubles

Answer 2

Ideal gas equation is $p V=n R T$
As volume is constant $p \propto T$
When $p'=2 p \rightarrow T'=2 T$
As $v_{r m s}^{2} \propto T', v_{r m s}^{2}$ doubles.