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When we measure the temperature of a substance by using a thermometer and waiting until the two come into thermal equilibrium, the thermometer will not display the original temperature of the substance before the thermometer was introduced - the measured temperature will be skewed a little depending on the thermometer's starting temperature. (For this same reason we cannot lower the temperature of a substance to absolute zero by repeated thermal contact with a substance already at absolute zero).

For most practical purposes this tiny inaccuracy due to the thermometer may not be of significance, but I am wondering if it is correct to say that a thermometer cannot actually measure the temperature of a substance?

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    $\begingroup$ MIT cooled objects down to 450 pK (0.45 nK) which is pretty low. $\endgroup$ – user6972 Apr 1 '14 at 3:05
  • $\begingroup$ There are thermometers work using radiation emitted by substance.. $\endgroup$ – Schrödinger's Cat Apr 1 '14 at 3:18
  • $\begingroup$ I don't think measurement is a problem in a calibrated system. I found a more recent experiment in 2013 where quantum gas was cooled below absolute zero. nature.com/news/quantum-gas-goes-below-absolute-zero-1.12146 $\endgroup$ – user6972 Apr 1 '14 at 8:16
  • $\begingroup$ @SachinShekhar The addition of the detector will upset the presumably thermal radiation distribution, changing the temperature of the object until the detector reaches equilibrium. At that point the temperature of the object being tested will have changed. $\endgroup$ – garyp Apr 1 '14 at 12:47
  • $\begingroup$ The comments on practicality and precision are all spot on, but I interpreted the spirit of the question as "theoretically possible". If I'm correct about the OP's intentions, then the discussions around practicality don't address the question. If I'm not correct, apologies to all for wasting space. :) $\endgroup$ – garyp Apr 1 '14 at 12:49
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Your description of the disturbance wrought on the system by the thermometer is sound. You may be able lessen the effect with a thermal diffusion model of the thermometer and by calculating what the system's temperature was before it brought the thermometer into equilibrium with itself, but for that approach to work, one must know the system's heat capacity (and the thermometer's temperature before the measurement). Measurements always disturb systems in the way you describe; this is the the Observer Effect and, although this is not to be confused with Heisenberg's uncertainty principle, historically Heisenberg began thinking about measurement uncertainty along the lines of an "Observer effect". He didn't stop there of course and his work and that which followed ultimately led mainstream physics to develop the separate famous uncertainty principle with its full blown denial of counterfactual reality (the idea that measurement outcomes before the measurement have a separate reality).

Is your statement that a thermometer can't really measure something's temperature correct? Strictly speaking, it is always true, as it is true of any instrument. But a more practical question is "is it misleading" or "does it give the right impression for the experiment at hand"; questions that are best handled by theoretical calculations and overbounding of the effect. Thus, if you are using a thermometer to measure the temperature of a swimming pool, then your statement, although strictly true, gives an utterly misleading idea of the thermometer's usefulness for that task. However, your statement is very practically true - anything else would be misleading - for the measurement of the temperature of a cubic centimetre of liquid if your purposes call for $\pm1^o\,\text{K}$ accuracy. For very small things, infrared thermometers are useful: these can measure the blackbody spectrum of an emitter, but one must take care that they are not contaminated by the radiation from other things nearby. This would be the approach you might try for a cubic centimetre, or, if you get really good at experimental measurement, a cubic millimetre of substance.

Experimental design for very precise measurements is often mostly about lessenning the observer effect for the experiment at hand; ultimately it all boils down to a thorough investigation of the theoretically expected signal to noise ratio your measurement setup and whether the foreseen SNR works for your purposes, as well as a statistical analysis of your measurement as it is repeated to check experimentally whether your theoretical SNR analysis is sound.

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I think that you can state that it can not measure the temperature of a substance before it have been test but it can measure the temperature after it have come in equilibrium with the substance.

For example, in an experiment that need to push a liquid to T temperature, what you do is heat up the liquid with the thermometer already inside. With this you avoid the problem of the thermometer having another temperature of the liquid, and it will mark the temperature correctly.

And as @WetSavannaAnimal said in its answer, when you need accuracy in an experiment what you try is to avoid the changes that make when you try to observe the experiment.

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  • $\begingroup$ Up voted. This looks like the best answer to me. $\endgroup$ – garyp Apr 1 '14 at 12:51
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It is correct to say that a thermometer cannot measure the temperature of an object accurately.You must reflect deeply on the fact that all the laws and measurements that we have in physics are some sort of approximations .Since matter is made of elementary particles this distinction of thermometer and the body whose temperature is to be measured are itself approximations.

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yes, it can, because you can adjust for the mentioned effects, at least in theory.

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