Relaxation time: Difference between revisions

Latest revision as of 05:19, 27 March 2024

In general, the time interval required for a system exposed to some discontinuous change of environment to undergo the fraction (1 - e^-1), or about 63%, of the total change of state that it would exhibit after an infinitely long time.
For example, a thermometer initially at equilibrium in a bath at temperature T₁ will exhibit an exponential change of temperature with time after being suddenly plunged into a bath at temperature T₂, theoretically assuming the new temperature T₂ only after an infinitely long time. The finite time interval required for the thermometer to undergo a change of amount (T₁ - T₂)(1 - e^-1) is called the thermal relaxation time of the thermometer. Occasionally, the fraction 9/10 is used in place of (1 - e^-1), so contexts must always be checked to be certain of the definition employed in a given case. The definition may also change for an underdamped device. The change of state of such a device may oscillate several times while approaching its final value.

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+In general, the time interval required for a system exposed to some discontinuous  change of [[environment]] to undergo the fraction (1 - ''e''<sup>-1</sup>), or about 63%, of the total [[change of state|change of  state]] that it would exhibit after an infinitely long time.<br/> For example, a [[thermometer]] initially at [[equilibrium]] in a bath at [[temperature]] ''T''<sub>1</sub> will exhibit  an exponential change of temperature with time after being suddenly plunged into a bath at  temperature ''T''<sub>2</sub>, theoretically assuming the new temperature ''T''<sub>2</sub> only after an infinitely long time.  The finite time interval required for the thermometer to undergo a change of amount (''T''<sub>1</sub> - ''T''<sub>2</sub>)(1  - ''e''<sup>-1</sup>) is called the thermal relaxation time of the thermometer. Occasionally, the fraction 9/10  is used in place of (1 - ''e''<sup>-1</sup>), so contexts must always be checked to be certain of the definition  employed in a given case. The definition may also change for an underdamped device. The change  of state of such a device may oscillate several times while approaching its final value.
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-== relaxation time ==
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-<div class="definition"><div class="short_definition">In general, the time interval required for a system exposed to some discontinuous  change of [[environment]] to undergo the fraction (1 - ''e''<sup>-1</sup>), or about 63%, of the total [[change of  state]] that it would exhibit after an infinitely long time.</div><br/> <div class="paragraph">For example, a [[thermometer]] initially at [[equilibrium]] in a bath at [[temperature]] ''T''<sub>1</sub> will exhibit  an exponential change of temperature with time after being suddenly plunged into a bath at  temperature ''T''<sub>2</sub>, theoretically assuming the new temperature ''T''<sub>2</sub> only after an infinitely long time.  The finite time interval required for the thermometer to undergo a change of amount (''T''<sub>1</sub> - ''T''<sub>2</sub>)(1  - ''e''<sup>-1</sup>) is called the thermal relaxation time of the thermometer. Occasionally, the fraction 9/10  is used in place of (1 - ''e''<sup>-1</sup>), so contexts must always be checked to be certain of the definition  employed in a given case. The definition may also change for an underdamped device. The change  of state of such a device may oscillate several times while approaching its final value.</div><br/> </div>
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