5. (5 pts) In class you measured/fit a thermometer response to a step change in the water temperature. The fit appeared to follow a 1" order response. Below is a sketch of a cross section of the thermocouple (pink) with a thin metal sheath (green hatched). The measured temperature is T(t) and at steady state it is the same as the ambient temperature, Tat). When the ambient temperature changes there is heat being exchanged until the thermocouple temperature, T(t), equilibrates with the ambient temperature. The heat exchanged can be given by the qct) equation, where U is the overall heat transfer coefficient and A is the surface area for heat transfer. You may assume before any disturbance occurs, the measured temperature, T(t), is at a constant temperature, which is not zero. Also, assume that over the range of temperature variations, the heat capacity of the thermocouple is constant, as is the overall heat transfer coefficient. The mass of the thermocouple is known (m) and the mass of the thin metal sheath may be neglected. 964 = UA(TACE) --TC) -TCE) Ta (6) 8 (5) d. Lastly, what is the thermocouple transfer function that shows how the deviation thermocouple temperature responds to changes in the deviation ambient temperature? Note no controller is involved in this transfer function. r(8) - [? G(s) Ta(s)