## 1 Introduction
### The EGT as a Parameter Useful for Indirectly Measuring the Engine Performances  
The starting point for the development of such an acquisition system is the individuation of the engine parameters to gather and the assessment of the best data-collection methods to employ. Studies dealing with ICEs [26; 27; 28; 29; 30; 31] usually focus on the following variables, which are the most representative of an engine and its operating conditions:  
* Torque;
* Engine speed;
* Fuel consumption;
* Air requirement;
* Mechanical, thermodynamic, total efficiency;
* Pollutant emissions;
* Lubricant quality;* Engine and cooling system temperatures;
* Exhaust gas temperature;
* Sound emissions and vibrations. Among all these parameters, this article will focus on the exhaust gas temperature (EGT). Indeed, EGT is one of the most meaningful parameters that can be acquired because it is representative of many phenomena occurring inside the engine (specifically, within the combustion chambers), and it is responsible for the correct operation of the devices located along the exhaust pipeline [33]. From a thermodynamic point of view, the EGT can be correlated with: engine torque, power and efficiency, combustion quality, and pollutant emissions. In addition, EGT can rightfully be assumed as an indicator of possible malfunctions involving all previous-listed quantities related to the engine or to the technical devices relying on EGT (the turbocharger, every pollutants-abatement systems: EGR, DPF, SCR, catalytic converters etc.). In particular, the relation between EGT and engine torque (\(M\)) is very important, and it is one of the reasons why EGT is such an interesting parameter to be gathered. \(M\) is a difficult parameter to be measured if there is no built-in sensor in the studied machine (esp. in the oldest ones), but its direct or indirect acquisition is fundamental as it can describe the engine output better than other parameters. One way to cope with this issue is to derive the torque value from the EGT that can be acquired through the use of thermocouples (from now on: TCs), that are almost inexpensive and very easy to install in comparison to a traditional torque-metering system. The temperature of the combustion gases reached at the discharge phase of a compression-ignition cycle (i.e., at the outlet of the exhaust valve in the motor head) is directly related (please refer to Figure 1):  
* To all the thermodynamic transformations composing the cycle before arriving at expansion 3-4, ideally adiabatic (in particular, also to the amount of fuel injected in the considered cycle, during the ideally-isobaric transformation 2-3), and also to the free expansion of combustion gases from point 4 at the exhaust valve opening, ideally isochoric;
* To the area included in the loop representing the whole cycle on a \(p\)-\(V\) plane (pressure-volume), equal to the work per cycle performed by the engine and, hence, to the torque [34]. For a given compression ratio \(r_{0}\) (constructive-geometric feature of an engine), the values of maximum pressure \(p_{2}=p_{3}\) and volume \(V_{4}=V_{1}\) that bound geometrically the curve of the adiabatic expansion 3-4 are fixed [34]. Consequently, the work per cycle, hence  
Figure 1: Ideal diesel cycle (i.e., related to a closed system processing an ideal fluid). The different heat \(Q\) supplied during the transformation 2–3. Ideally, isobar is responsible for the different work-per-cycle expressed by the system and gives different temperatures \(T\) at the end of the cycle. the torque expressed by an engine and the final temperature reached by the operating fluid, which is related to the EGT in an open system (\(T_{ex}\cong T_{4}\)), depends only on the amount of heat supplied to the fluid (Figure 1). Furthermore, in a real thermodynamic cycle, there is also a dependency of the torque from the rotational speed (through the volumetric efficiency).