Do you need temp calibration on a ph meter ?
Strictly speaking, no but if you do have it it can be a big convenience, particularly during calibration. If you do not have it then either both buffers must be at the same temperature and the sample must be at the same temperature as the buffers or you must do yourself the math required to interpret and correct the buffer readings and the sample readings.
If you do use ATC you should still try to have the buffer and sample temperatures pretty close so that the ATC doesn't have to do too much. Proper functioning of ATC depends on the isolelectric pH (the pH at which the electrodes response does
not repond to temperature being 7. ATC introduced by isoelectric pH being different from 7 are small but increase with the temperature differences.
The voltage produced by a pH electrode is
E = Ei + Un*T*(pH - pHi)
where Ei is the voltage it produces when immersed in a solution of pH equal to pHi, the isoelectric pH, Un is the Nerst coefficient and T the temperature of the solution in Kelvins. Un*T has value -58.67 mV/pH at 20 °C. Note that Un*T is the theoretical response. A real electrode will have a slope of lesser magnitude than 58.67 and it is the role of calibration to determine what that slope is as well as the value for Ei. That's why 2 buffers are used: 2 equations in 2 unknowns.
The equation shows that the response of the meter is directly proportional to temperature. But pH can be a function of temperature as well. The nature of the dependence is usually, as is the case with wort, decreasing pH with increasing temperature. It's widely accepted that wort/mash has a pH lower at mash temperature by about 0.2 pH than it is at room temperature but that depends on the nature of the grist and the mineral content of the water. In some cases the opposite is true. The pH of the typical pthalate pH 4 buffer is 4.002 at 20 °C but is 4.125 at 70 °C. OTOH the phosphate buffer usually used for pH 7 has pH 7.017 at 20 °C and 6.981 at 70 °C i.e. a drop but one of small magnitude compared to wort and the pH 4 buffer.
The usual explanation for pH drop with increasing temerature is that it takes less energy to abstract a proton from an acid at higher temperaure as all the parts of a molecule are in a higher energy state from the thermal induced motion. I.e. the pK's of the acids involved drop and so, thus, does the pH.
Given the various ways pH changes with temperature I'm not sure I believe the log(log(temp)) rule. IIRC the variation is pretty linear for wort. For pH 4 buffer pH(K) = 1617.3/K - 9.2852 + 0.033311*K - 2.3211e-5*K*K, with K being the temperature in Kelvins, describes the variation pretty well.
