Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Medical
  • Consider a gas system composed of 1100 particles, each with the following speed distribution: • 1000 particles with a speed of 100 m/s each, • 2000 particles with a speed of

Consider a gas system composed of 1100 particles, each with the following speed distribution:
• 1000 particles with a speed of 100 m/s each,
• 2000 particles with a speed of 200 m/s each,
• 4000 particles with a speed of 300 m/s each,
• 3000 particles with a speed of 400 m/s each,
• 1000 particles with a speed of 500 m/s each.
Calculate the average speed and the root mean square (rms) speed of the gas system.

Option: 1

2175.34m/s
 


Option: 2

958.70m/s
 


Option: 3

452.200 m/s
 


Option: 4

142.20 m/s


Answers (1)

best_answer

Let n_i denote the number of particles with speed v_i, where i represents the speed category. The total number of particles, N, is 1100.
The average speed  ?v can be calculated using the formula:

\bar{v}=\frac{1}{N} \sum_i n_i v_i

Substituting the given values, we have:

\begin{aligned} \bar{v} & =\frac{1}{1100}(1000 \cdot 100+2000 \cdot 200+4000 \cdot 300+3000 \cdot 400+1000 \cdot 500) \\ & =\frac{1}{1100} \cdot 2200000 \\ & \approx 2000 \mathrm{~m} / \mathrm{s} . \end{aligned}

The root mean square (rms) speed v_{rms} can be computed using the formula:

v_{\mathrm{rms}}=\sqrt{\frac{1}{N} \sum_i n_i v_i^2} .
Substituting the given values, we get:

\begin{aligned} v_{\mathrm{rms}} & =\sqrt{\frac{1}{1100}\left(1000 \cdot 100^2+2000 \cdot 200^2+4000 \cdot 300^2+3000 \cdot 400^2+1000 \cdot 500^2\right)} \\ & =\sqrt{\frac{1}{1100} \cdot 5206000000} \\ & \approx \sqrt{4732727.27} \\ & \approx 2175.34 \mathrm{~m} / \mathrm{s} . \end{aligned}Hence, the average speed of the gas system is approximately 2000 m/s, and the root mean square speed is approximately 2175.34 m/s.
Therefore, the correct option is 1.

Posted by

Gautam harsolia

View full answer

NEET 2024 Most scoring concepts

    Just Study 32% of the NEET syllabus and Score up to 100% marks

Similar Questions

Trending Articles/News

anam-khan

'PM Modi personally supervising the situation': Centre tells SC in NEET case
anam-khan

NEET Paper Leak Row: NTA informs SC of security overhaul, institutional reforms
anam-khan

Re-NEET 2026 City Intimation Slip LIVE: NTA MBBS admit card soon; direct link, login details, exam date

Latest Question