### Dynamic Response » Transfer Functions and the Transfer-Function Diagram » Example: Temperature Response

As an example, consider a liquid-in-glass thermometer immersed at time t_{0} = 0 into a bath of fluid having temperature T_{F} (the final bath temperature). If the thermometer reads T_{0} before immersion, it will start to move toward T_{F} after immersion and will display a temperature T(t) that moves toward T_{F} over some period of time. The rate at which heat is transferred to the thermometer depends on the temperature difference T(t) - T_{F}, often in a linear relationship, so the displayed temperature will move faster at first and gradually move more slowly toward T_{F} as the temperature difference becomes small.

A linear relationship between the time rate of change in temperature and the temperature difference between the sensor and the bath can be represented by a first-order linear differential equation like dT(t) / dt = (T_{F} - T(t)) / 𝜏, where 𝜏 is a constant that determines the rate at which the sensor responds to its environment and T_{F} is the final temperature. This equation has an exponential solution, such that T(t) approaches T_{F} but never reaches that value, as shown in the figure. This first-order response is characteristic behavior for many sensors and electronic components of sensors.

The response of a first-order sensor with time constant 1. The temperature to which the sensor is exposed (x) is shown as the green line and the measured temperature (M) as the blue line. At t = 0, x abruptly changes from 0 to T_{f} = 1. Image from NCAR/EOL.

#### Question

Select whether the statement refers to a static performance characteristic or a dynamic performance characteristic.

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