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  • A gas system consists of 1100 particles, 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,

A gas system consists of 1100 particles, 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

657.60 m/s


Option: 2

1487.30 m/s


Option: 3

455.50 m/s


Option: 4

2175.34 m/s


Answers (1)

best_answer

Let ni represent the number of particles with speed vi, where i denotes the speed category. The total number of particles, N, is 1100. The average speed \vec{v} can be calculated using the formula:

                \vec{v} = \frac{1}{N}\sum_{i}^{} n_{i}v_{i}

Substituting the given values, we have:

\vec{v} = \frac{1}{1100}(1000 * 100 + 2000 * 200 + 4000 * 300 + 3000 * 400 + 1000 * 500)

    = \frac{1}{1100} * 2200000

       \approx 2000 m/s

The root mean square (rms) speed vrms can be computed using the formula:

                v_{rms} = \sqrt{\frac{1}{N} \sum_{i}^{} n_{i}v_{i}^{2}}

Substituting the given values, we get:

v_{rms} = \sqrt{\frac{1}{1100} (1000 * 100^2 + 2000 * 200^2 + 4000 * 300^2 + 3000 * 400^2 + 1000 * 500^2)}            = \sqrt{\frac{1}{1100} * 5206000000}

            \approx \sqrt{4732727.27}

            \approx 2175.34 m/s

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.

Posted by

Gautam harsolia

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