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  • A gas-filled container with dimensions 0.4 m * 0.5 m * 0.6 m is held at a temperature of 300 K. The gas consists of 6.0 * 1023 gas molecules. Each molecule has a mass of 2

A gas-filled container with dimensions 0.4 m * 0.5 m * 0.6 m is held at a temperature of 300 K. The gas consists of 6.0 * 1023 gas molecules. Each molecule has a mass of 2.5 * 10−26 kg. Calculate the average force exerted by the gas molecules on the walls of the container, considering perfectly elastic collisions.

Option: 1

547 * 106 N


Option: 2

2.47 * 104 N


Option: 3

5.67 * 105 N


Option: 4

3.82 * 103 N


Answers (1)

best_answer

Given data:

Length of the container (L) = 0.4 m
Width of the container (W) = 0.5 m
Height of the container (H) = 0.6 m
Temperature (T) = 300 K
Number of molecules (N) = 6.0 × 1023
Mass of each molecule (m) = 2.5 * 10−26 kg
Boltzmann constant (k) = 1.38 * 10−23 J/K

Step 1: Calculate the volume of the container:

                V = L * W * H

               V = 0.4 * 0.5 * 0.6

                V = 0.12 m3

Step 2: 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}*300}{2.5*10^{-26}}}

            v_{rms} \approx 517.24 m/s                    

Step 3: 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}}{V}

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

                F = \frac{26.0*10^{23} * 2.5*10^{-26}*(517.24)^{2}}{0.12}

                F \approx 5.67 * 10^{5} N

Posted by

shivangi.bhatnagar

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