i had always thought the temperature the a substance to be a measure up of the typical kinetic energy of the corpuscle in that substance:

$E_k = (3/2) k_bT$

where $E_k$ is the average kinetic energy of a molecule, $k_b$ Boltzmann"s constant, and $T$ the temperature. (I"m not certain of the 3/2 coefficient.) Then i heard from numerous folks the this is a simplistic notion, not strictly true, however they didn"t described what they believed was flawed v this idea. I"d like to understand what (if anything) is objectionable around this idea? Is it that the device must it is in macroscopically in ~ rest? Is it the it ignores the quantum mechanically compelled motion that particles that persists at short temperatures? once is it no valid?

There room a variety of ways of defining temperature, for example using:

$$partial S over partial E = 1over T$$

This meaning is the basis of an adverse temperatures. This is a instance where the temperature is no a measure of average kinetic energy.

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The expression your created down because that the power is the expression because that the ensemble average kinetic power of a monatomic right gas. Therefore, we check out that for this system, the average energy of the mechanism is just proportional to the temperature.

For a basic statistical mechanical system, however, it could not even make feeling to talk about the "average kinetic energy" of the system. Because that example, take a quantum mechanism consisting that a solitary spin $1/2$ particle communicating with a magnetic field. That is possible to specify a temperature because that this device when that is in contact with a warmth bath even if the bit is not moving around. In together cases, one appeals to an ext general meanings of temperature such together that come which john Rennie ad in his answer.

temperature the a substance to be a measure up of the mean kinetic energy of the corpuscle in the substance

This is only true because that a monatomic gas. Also without quantum mechanics, a timeless diatomic gas has actually three much more degress of flexibility than a monatomic gas—two rotational and also one vibrational—for a complete of 6. The equipartition organize tells us that the kinetic power will be split equally among these. For this reason the kinetic energy of the gas corpuscle in this situation represents only 1/2 the the power represented through the temperature.

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