C Response of a Temperature Measuring Element

Instrument measurement response can often be important in the overall system response. The thermal response of a simple thermometer bulb, immersed in fluid, as shown in Fig. 2.6, is the result of a simple heat balance in which 

Often an instrument response measurement can be fitted empirically to a first-order lag model, especially if the pure instrument response to a step change disturbance has the general shape of a first-order exponential. 

As shown in Section 2.1.1.1, the time constant for the instrument is then given as the time at which 63% of the final response is achieved and the instrument response may be described by the simple relationship 

The ratio of the time constants, Tmeas and Tgygtem, determines whether or not the system value is significantly different from the measurement value when conditions are changing, since the measured value will tend to lag behind that of the system. 

For a thermometer to react rapidly to changes in the surrounding temperature, the magnitude of the time constant should be small. This involves a high 

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