At what temperature in Kelvin is the rms speed of hydrogen molecules the same as oxygen molecules at 1327 degrees * C?

Answer (Detailed Solution Below)

Option 3 : 6495°C

Concept:

Root Mean Square Speed

• It is defined as the square root of the mean of squares of the speed of different molecules.
• The root-mean-square speed takes into account both molecular weight and temperature, two factors that directly affect the kinetic energy of a material.
• The rms speed of any homogeneous gas sample is given by:

Where R = universal gas constant, T = temperature and M = Molecular mass

Calculation:

Let velocity of oxygen = Vo

Let velocity of hydrogen = Vh

Molecular weight of oxygen Mo = 32

Molecular weight of hydrogen Mh = 2

Let the required temperature be T0 = 

Temperature of hydrogen TH =  150 °C = 150 + 273 = 423 K

Now

Equating

Squaring and cancling constant terms 

we get

⇒ To = 16 Th

⇒ To = 16 × 423 K = 6768 K

This temperature in °C will be 6768  -  273 = 6495°C

So, the correct option is 6495°C.

Mistake Points

Aspirants make take the temperature in °C. It should be taken in Kelvin, the SI unit for any calculation purpose. 

Win over the concepts of The Kinetic Theory of Gases and get a step ahead with the preparations for Physics with Testbook.

India’s #1 Learning Platform

Start Complete Exam Preparation

Video Lessons & PDF Notes

Get Started for Free Download App

Trusted by 2,98,18,858+ Students

Tardigrade - CET NEET JEE Exam App

© 2022 Tardigrade®. All rights reserved

>

At what temperature is the rms velocity of a hydrogen molecule equal to that of an oxygen molecule at 47∘ CA. 80 KB. 73 KC. 3 KD. 20 K

>

At what temperature is the rms speed of hydrogen molecules the same as that of oxygen molecules at 1327∘C ?