Thermal loading by a contact temperature sensor

Thermal loading by a contact temperature sensor is the disturbance of an object's temperature caused by exchanging heat with the temperature sensor used to measure it. A sensor initially colder than a small object draws heat from the object: the final reading can be accurate for the disturbed system while differing from the object's original temperature.

An illuminating idealization treats the object and sensor as two uniform bodies with constant heat capacities $C_o$ and $C_s$, joined by thermal conductance $G$ and isolated from everything else. Their energy conservation equations areAdding the equations shows that $C_o{T}_o+C_s{T}_s$ is constant. Consequently,For $C_o=0.20J/K$, $C_s=0.020J/K$, $T_{o0}=80{}^{\circ }\mathrm{C}$ and $T_{s0}=20{}^{\circ }\mathrm{C}$, the common equilibrium is $74.55{}^{\circ }\mathrm{C}$. The measurement has cooled the object by about $5.45\mathrm{K}$.

Subtracting the two differential equations gives an exponentially decaying temperature difference with time constantIncreasing the contact thermal conductance makes the disturbance happen faster without changing this isolated model's final equilibrium. Reducing the sensor heat capacity reduces the disturbance. A real object also exchanges heat with its surroundings, while sensor leads can provide another heat transfer path.

An electrically read sensor can additionally generate Joule heating. That is a separate loading mechanism: the thermometry guide measures resistance-thermometer self-heating by changing the measuring electric current and extrapolating toward zero dissipated electric power.^[ref]