Chapter 19: Q33P (page 579)

The speeds of 10molecules are $2.0, 3.0, 4.0, \dots ., 11 \frac{k m}{s}$
What are their average speeds?
What are their rms speeds?

Short Answer

Expert verified

Step by step solution

Given data

The speeds of 10 molecules are, $2.0, 3.0, 4.0, \dots \dots \dots \dots \dots, 11 \frac{km}{s} .$

Understanding the concept

Average speed is calculated by adding the speed of each molecules and then by dividing the total number of molecules.

The RMS speed of molecules is given by,

$v_{r m s} = \sqrt{\frac{\sum_{}^{} v^{2}}{N}}$

(a) Calculate the average speeds

The average speed of molecules is

$\begin{matrix} \bar{v} = \frac{\sum v}{N} \\ \bar{v} = \frac{2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11}{10} \\ \bar{v} = 6.5 km / s \end{matrix}$

Therefore the average speed of molecules is $6.5 km / s$ .

(b) Calculate the rms speeds

The RMS speed of molecules is

$v_{r m s} = \sqrt{\frac{\sum_{}^{} v^{2}}{N}}$

Here,

$\begin{matrix} \sum v^{2} = 2^{2} + 3^{2} + 4^{2} + 5^{2} + 6^{2} + 7^{2} + 8^{2} + 9^{2} + 10^{2} + 11^{2} \\ = 505 {km}^{2} / s^{2} \end{matrix}$

Substitute $505 {km}^{2} / s^{2}$ for $\sum v^{2}$ and 10 for N into the above equation.

$\begin{matrix} v_{r m s} = \sqrt{\frac{505}{10}} \\ = 7.1 km / s \end{matrix}$

Therefore the RMS speed of the molecules is $7.1 km / s$ .

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The speeds of 10molecules are $2.0, 3.0, 4.0, \dots ., 11 \frac{k m}{s}$
What are their average speeds?
What are their rms speeds?

Short Answer

Step by step solution

Given data

Understanding the concept

(a) Calculate the average speeds

(b) Calculate the rms speeds

One App. One Place for Learning.

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The speeds of 10molecules are2.0,3.0,4.0,….,11kmsWhat are their average speeds?What are their rms speeds?

Short Answer

Step by step solution

Given data

Understanding the concept

(a) Calculate the average speeds

(b) Calculate the rms speeds

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fields in Physics

Measurements

Further Mechanics and Thermal Physics

Scientific Method Physics

Waves Physics

Nuclear Physics

Study anywhere. Anytime. Across all devices.

The speeds of 10molecules are $2.0, 3.0, 4.0, \dots ., 11 \frac{k m}{s}$
What are their average speeds?
What are their rms speeds?