Question

3. The r.m.s velocity of hydrogen gas molecules at N.T.P. is v m/se. the gas is heated at constant volume till
the pressure becomes 4 times. The final r.m.s. velocity is,
(A) v/2​

Answer 1

Given :

The rms velocity of hydrogen gas molecules at N.T.P. is v m/s.

The gas is heated at constant volume till the pressure becomes 4 times.

To Find :

Final rms velocity of the gas.

Solution :

Let initial pressure of the gas be P.

ATQ, final pressure will be 4P.

❖ RMS velocity of the gas at temperature T is given by

$\dag\:\underline{\boxed{\bf{\orange{V_{rms}=\sqrt{\dfrac{3PV}{M}}}}}}$

• M denotes molar mass of the gas

Here volume of the gas and molar mass remain constant so we can say that

$\dag\:\underline{\boxed{\bf{\gray{V_{rms}\varpropto\sqrt{P}}}}}$

➙ v₁ / v₂ = √P₁ / √P₂

➙ v / v₂ = √P / √4P

➙ v₂ = √4 × v

➙ v₂ = 2v

Knowledge BoosteR :

• At high temperature or low pressure the molecules of gas are far apart and molecular interactions are negligible, without interactions the gas behaves as an ideal gas.
• Avogrado hypothesis the equality of molecules in equal volumes of gas at a fixed temperature and pressure.

Answer 2

Answer:

The correct answer is v/2