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  • A cubical container with sides of 0.2 m is filled with an ideal gas at a temperature of 400 K. The gas consists of 5.0 * 1023 gas molecules. Each molecule has a mass of 2.0 * 10<sup

A cubical container with sides of 0.2 m is filled with an ideal gas at a temperature of 400 K. The gas consists of 5.0 * 1023 gas molecules. Each molecule has a mass of 2.0 * 10−26 kg. Calculate the average force exerted by the gas molecules on the walls of the container, considering perfectly elastic collisions.

Option: 1

9.24 * 107 N


Option: 2

5.47 * 105 N


Option: 3

5.03 * 105 N


Option: 4

3.25 * 106 N


Answers (1)

best_answer

Given data:

Side length of the container (L) = 0.2 m
Temperature (T) = 400 K
Number of molecules (N) = 5.0 * 1023
Mass of each molecule (m) = 2.0 * 10−26 kg
Boltzmann constant (k) = 1.38 * 10−23 J/K

Step 1: Calculate the root mean square (rms) speed of the gas molecules. The rms speed is given by the formula:

            v_{rms}= \sqrt \frac{3kT}{m}

Substitute the given values and solve for vrms:

                    v_{rms}= \sqrt \frac{3*1.38*10^{-23}*400}{2.0*10^{-26}} \approx 1005.15 m/s

Step 2: Calculate the average force exerted by the gas molecules on the walls of the container. The average force can be calculated using the formula:

                 F = \frac{2mNv^{2}_{rms}}{L}

Substitute the given values and the calculated vrms and solve for F:

F = \frac{2*5.0*10^{23}*2.0*10^{-26}*(1005.15)^{2}}{0.2}       \approx 5.03 * 10^{5} N

Posted by

Suraj Bhandari

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