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According to the kinetic molecular theory, what distinguishes the movement of molecules in gases compared to those in solids and liquids?
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7. Gases
Kinetic Molecular Theory
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According to the kinetic molecular theory, what happens to the average speed of gas molecules when the temperature decreases?
A
The average speed of the molecules decreases.
B
The average speed of the molecules increases.
C
The average speed of the molecules remains unchanged.
D
The average speed of the molecules fluctuates randomly.
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Recall that according to the kinetic molecular theory, the average kinetic energy of gas molecules is directly proportional to the absolute temperature (in Kelvin). This relationship is given by the equation: \(\frac{1}{2} m v_{\text{avg}}^2 = \frac{3}{2} k_B T\), where \(m\) is the mass of a molecule, \(v_{\text{avg}}\) is the average speed, \(k_B\) is Boltzmann's constant, and \(T\) is the temperature.
Understand that since the average kinetic energy depends on temperature, a decrease in temperature means a decrease in the average kinetic energy of the gas molecules.
Recognize that the average speed \(v_{\text{avg}}\) of the molecules is related to the kinetic energy by rearranging the equation: \(v_{\text{avg}} = \sqrt{\frac{3 k_B T}{m}}\).
From this equation, observe that the average speed is proportional to the square root of the temperature, so if temperature decreases, the average speed decreases as well.
Therefore, conclude that when the temperature decreases, the average speed of gas molecules decreases according to the kinetic molecular theory.
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