The molecules of a given mass of gas have RMS velocity of 200 m  s - 1 at 27 o C and 1.0 × 10 5   N  m - 2 pressure. When the temperature and pressure of the gas are respectively, 127 o C and 0.05 × 10 5   N  m - 2 , the r.m.s. velocity of its molecules in m  s - 1 is:

Step-by-step solution

RMS speed of molecules is V RMS = 3 R T M , where R is universal gas constant, T is absolute temperature and M is molar mass of gas. So it depends only on temperature, V r m s ∝ T ⇒ V 1 V 2 = T 1 T 2 ⇒ 200 V 2 = 300 400 ⇒ 200 V 2 = 3 2 ⇒ V 2 = 400 3   m   sec - 1