
The root mean square speed of a gas of density 1.5 g/ litre at a pressure of is $2\times {10^6}~{N}{m^{-2}}$?
Answer
164.1k+ views
Hint: Gases are composed of atoms or molecules that flow in random directions at variable rates. The root mean square velocity (RMS velocity) is a method for calculating a single velocity for the particles. The root mean square velocity formula is used to calculate the mean velocity of a gas particle.
Complete answer:
We can see from the root mean square speed formula that changes in molar mass and the temperature impact the pace of gas molecules. The speed of molecules in a gas is related to temperature and inversely related to the gas's molar mass. In other words, when the temperature of a gas sample rises, the molecules accelerate, and the root mean square molecular speed rises as well.
In the given question, we need to find out the root mean square speed, when density of the gas is equal to $1.5g/litre$ and the pressure of the gas is $2\times {{10}^{6}}N/{{m}^{2}}$
The formula of the root mean square velocity can be written as:
$\overline{c}=\sqrt{\dfrac{3P}{\rho }}$
Where $P$ is the pressure of the gas and $\rho $is the density of the gas.
$\Rightarrow \sqrt{\dfrac{3\times 2\times {{10}^{6}}}{1.5}}$
$\Rightarrow 2\times {{10}^{3}}m/s$
Hence the root mean square speed of the given is $2\times {{10}^{3}}m/s$.
Note: The RMS computation yields the root mean square speed rather than the velocity. This is due to the fact that velocity is a vector quantity with magnitude and direction and speed is the scalar quantity with only magnitude. The RMS computation provides simply the magnitude or speed.
Complete answer:
We can see from the root mean square speed formula that changes in molar mass and the temperature impact the pace of gas molecules. The speed of molecules in a gas is related to temperature and inversely related to the gas's molar mass. In other words, when the temperature of a gas sample rises, the molecules accelerate, and the root mean square molecular speed rises as well.
In the given question, we need to find out the root mean square speed, when density of the gas is equal to $1.5g/litre$ and the pressure of the gas is $2\times {{10}^{6}}N/{{m}^{2}}$
The formula of the root mean square velocity can be written as:
$\overline{c}=\sqrt{\dfrac{3P}{\rho }}$
Where $P$ is the pressure of the gas and $\rho $is the density of the gas.
$\Rightarrow \sqrt{\dfrac{3\times 2\times {{10}^{6}}}{1.5}}$
$\Rightarrow 2\times {{10}^{3}}m/s$
Hence the root mean square speed of the given is $2\times {{10}^{3}}m/s$.
Note: The RMS computation yields the root mean square speed rather than the velocity. This is due to the fact that velocity is a vector quantity with magnitude and direction and speed is the scalar quantity with only magnitude. The RMS computation provides simply the magnitude or speed.
Recently Updated Pages
Uniform Acceleration - Definition, Equation, Examples, and FAQs

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

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

Class 11 JEE Main Physics Mock Test 2025

JEE Main Chemistry Question Paper with Answer Keys and Solutions

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

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
