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The gas temperature at which the root mean square velocity of hydrogen exceeds their most probable velocity is:

a. Infinity
b. Zero Kelvin
c. Room temperature
d. Critical temperature

User Inconnu
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1 Answer

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Final answer:

The root-mean-square speed of gas molecules always exceeds their most probable speed by definition, regardless of temperature, thus making this comparison temperature-independent. There is no specific temperature at which rms speed overtakes the most probable speed.

Step-by-step explanation:

The student's question pertains to the comparison of root-mean-square (rms) speed and most probable speed (peak speed) of hydrogen molecules at different temperatures. By definition, the rms speed, which is the square root of the average of the square of the velocity, will always exceed the most probable velocity. This is because the most probable speed corresponds to the speed at which the number of molecules is maximized in a Maxwell-Boltzmann distribution, whereas the rms speed is a measure of the average energy of the gas particles and therefore includes velocities that are both higher and lower than the most probable speed.

The relationship between temperature and these speeds does not lead to a temperature at which the rms speed exceeds the most probable speed; it is intrinsic to the definitions that the rms speed is higher.

Absolute zero is the theoretical temperature at which motion of particles theoretically ceases and it is defined as 0 Kelvin or -273.15°C. It is important when discussing gas laws and the behavior of gases at low temperatures. However, this temperature does not relate to the point at which rms speed exceeds the most probable speed, as that comparison is not temperature dependent.

User Rizerzero
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