måndag 7 januari 2013

Measuring Temperature vs Emissivity

In a previous posts I showed that an ideal blackbody 1 of temperature T_1 can be used as a reference thermometer capable of measuring the temperature T_2 of a given body 2 through radiative equilibrium:
  • alpha_2 sigma T_ 1^4 = beta_2 sigma T_2^4
where alpha_2 is the absorptivity of 2, epsilon_2 is the emissivity of 2, and 
  • alpha_2 sigma T_ 1^4 is the energy absorbed by 2,
  • beta_2 sigma T_2^4 is the energy emitted by 2.
Knowing that alpha_2 = epsilon_2 makes it possible to assign the temperature T_2 = T_1 to the given body from radiative equilibrium with the reference blackbody thermometer showing T_1.

Is it possible to also measure also the emissivity epsilon_2 (=alpha_2)? In the setting of the communicating vessels above, this means to measure the rate of the flow between the vessels as compared with measuring only the equal levels representing equal temperatures.

This would seem to equire non-equilibrium measurement  (since equilibrium only gives the temperature) recording the change of temperature of 1 while in radiative contact with 2 with T_2 different from T_1. Assuming T_2 > T_ 1, the rate of energy transfer from 2 to 1 would be
  • epsilon_2 sigma T_2^4 - alpha_2 sigma T_1^4
which could be measured as a rate of change of T_1. Would this allow to determine epsilon_2 (= alpha_2)? Not easily, because we have two quantities to determine, epsilon_2 and T_2, but only one condition, the rate of change of T_1. To sum up:
  • to measure temperature is easy (by equilibrium)
  • to measure emissivity is hard (by non-equilbrium).
This directly connects to the previous post. Lacking measurement of emissivity, it may be tempting to assume that it is equal to 1, which may mean fooling yourself.

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