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  • A container holds an ideal gas at a temperature of 400 K. The gas consists of 2.0 * 1023 gas molecules. Each molecule has a mass of 3.0 * 10−26 kg. Calculate the RMS spe

A container holds an ideal gas at a temperature of 400 K. The gas consists of 2.0 * 1023 gas molecules. Each molecule has a mass of 3.0 * 10−26 kg. Calculate the RMS speed of the gas molecules in all three directions (x, y, and z) and verify that they are the same.

Option: 1

658.88 m/s


Option: 2

605.45 m/s


Option: 3

795.41 m/s


Option: 4

462.12 m/s


Answers (1)

best_answer

Given data:

Temperature (T) = 400 K
Number of molecules (N) = 2.0 * 1023
Mass of each molecule (m) = 3.0 * 10−26 kg
Boltzmann constant (k) = 1.38 * 10−23 J/K

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

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

Substitute the given values and solve fror vrms:

            v_{rms} = \sqrt{\frac{3 * 1.38 * 10^{-23} * 400}{3.0 * 10^{-26}}}

                    v_{rms} \approx 658.88 m/s

Step 2: Calculate the RMS speed in all three directions. Since the RMS speed is the same in all directions, the RMS speed 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} = 658.88 m/s

Posted by

Shailly goel

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