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  • An ideal gas is contained in a cubic container with sides of length 0.2 m. The gas is at a temperature of 500 K. Calculate the RMS velocity of the gas molecules in all three directions (x, y, and z

An ideal gas is contained in a cubic container with sides of length 0.2 m. The gas is at a temperature of 500 K. Calculate the RMS velocity of the gas molecules in all three directions (x, y, and z) and verify that they are the same.

Option: 1

1587.21 m/s


Option: 2

1487.36 m/s


Option: 3

1356.69 m/s


Option: 4

1640.63 m/s


Answers (1)

best_answer

Given data:

Side length of the container (a) = 0.2 m
Temperature (T) = 500 K
Boltzmann constant (k) = 1.38 * 10−23 J/K

Step 1: Calculate the RMS velocity in one direction (vrms) using the formula:

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

Substitute the given values and the mass of a molecule (assume m = 2×10−26 kg) and solve for vrms:

v_{rms} = \sqrt{\frac{3*1.38*10^{-23}*500}{2*10^{-26}}}

            v_{rms} \approx 1640.63 m/s

Step 2: Calculate the RMS velocity in all three directions. Since the RMS velocity is the same in all directions, the RMS velocity in each direction (v^{x}_{rms},v^{y}_{rms},v^{z}_{rms}) will be equal to vrms calculated in Step 1.

v^{x}_{rms} =v^{y}_{rms} =v^{z}_{rms} = 1640.63 m/s

Posted by

Sanket Gandhi

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