
At the same temperature and pressure and volume of two gases, which of the following quantities is constant.
(A) Total number of molecules
(B) Average kinetic energy
(C) Root mean square velocity
(D) Mean free path
Answer
162.9k+ views
Hint:First start with finding the formula for all the given options such as formula for the average kinetic energy, root mean square velocity and the mean free path. Then try to understand what are the variable and constant quantity in the formula and finally you will get the required answer.
Complete answer:
Let start with Option(A):
Total number of the molecules of gas does not depends on the volume, pressure and temperature of the gas. Therefore, number of molecules is not constant.
Now, for Option(B):
We know that formula for the average kinetic energy of a gas is as follows;
${K_{avg}} = \dfrac{3}{2}{K_B}T$
Here, it is only depended on temperature of the gas molecule.
Hence the average kinetic energy is constant in this case.
Now, for Option(C):
We know; ${V_{rms}} = \sqrt {\dfrac{{3{k_B}t}}{m}} $
Here, it depends also on the m. Therefore, it is not constant.
Now, for Option(D):
We know; $\lambda = \dfrac{{{K_B}T}}{{\sqrt 2 \pi {d^2}P}}$
Here it also depended on the value of d. Therefore, it is not constant.
Hence the correct answer is Option(B).
Note: Formula for the average kinetic energy, root mean square velocity and the mean free path is needed in order to solve the particular question. Also note that here in the option average kinetic energy is mentioned if it is kinetic energy only then the value will not be constant hence the answer will get changed.
Complete answer:
Let start with Option(A):
Total number of the molecules of gas does not depends on the volume, pressure and temperature of the gas. Therefore, number of molecules is not constant.
Now, for Option(B):
We know that formula for the average kinetic energy of a gas is as follows;
${K_{avg}} = \dfrac{3}{2}{K_B}T$
Here, it is only depended on temperature of the gas molecule.
Hence the average kinetic energy is constant in this case.
Now, for Option(C):
We know; ${V_{rms}} = \sqrt {\dfrac{{3{k_B}t}}{m}} $
Here, it depends also on the m. Therefore, it is not constant.
Now, for Option(D):
We know; $\lambda = \dfrac{{{K_B}T}}{{\sqrt 2 \pi {d^2}P}}$
Here it also depended on the value of d. Therefore, it is not constant.
Hence the correct answer is Option(B).
Note: Formula for the average kinetic energy, root mean square velocity and the mean free path is needed in order to solve the particular question. Also note that here in the option average kinetic energy is mentioned if it is kinetic energy only then the value will not be constant hence the answer will get changed.
Recently Updated Pages
JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Main 2025 Session 2: Exam Date, Admit Card, Syllabus, & More

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Trending doubts
Degree of Dissociation and Its Formula With Solved Example for JEE

Charging and Discharging of Capacitor

Instantaneous Velocity - Formula based Examples for JEE

JEE Main Chemistry Question Paper with Answer Keys and Solutions

JEE Main Reservation Criteria 2025: SC, ST, EWS, and PwD Candidates

What is Normality in Chemistry?

Other Pages
Total MBBS Seats in India 2025: Government College Seat Matrix

NEET Total Marks 2025: Important Information and Key Updates

Neet Cut Off 2025 for MBBS in Tamilnadu: AIQ & State Quota Analysis

Karnataka NEET Cut off 2025 - Category Wise Cut Off Marks

NEET Marks vs Rank 2024|How to Calculate?

NEET 2025: All Major Changes in Application Process, Pattern and More
