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  • A cylindrical container with a radius of 0.15 m and a height of 0.4 m is filled with an ideal gas at a temperature of 600 K. The gas consists of 3.5 * 1023 gas molecules. Each molec

A cylindrical container with a radius of 0.15 m and a height of 0.4 m is filled with an ideal gas at a temperature of 600 K. The gas consists of 3.5 * 1023 gas molecules. Each molecule has a mass of 1.8 * 10−26 kg. Calculate the average force exerted by the gas molecules on the walls of the container, considering perfectly elastic collisions.

Option: 1

1.67 * 106 N


Option: 2

2.51 * 108 N


Option: 3

3.56 * 104 N


Option: 4

1.49 * 109 N


Answers (1)

best_answer

Given data:

Radius of the container (r) = 0.15 m
Height of the container (h) = 0.4 m
Temperature (T) = 600 K
Number of molecules (N) = 3.5 * 1023
Mass of each molecule (m) = 1.8 * 10−26 kg
Boltzmann constant (k) = 1.38 * 10−23 J/K

Step 1: Calculate the volume of the cylindrical container:

                V =\pi r^{2}h

Substitute and solve for V:

                V =\pi * (0.15)^{2} * 0.4

                V \approx 0.0283 m^{3}

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}*600}{1.8*10^{-26}}}

                v_{rms} \approx 1497.28 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{2*3.5*10^{23} *1.8*10^{-26}*(1497.28)^{2}}{0.0283}       F \approx 1.67 * 10^{6}N

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