A temperature measurement system consists of linear elements and has an overall steady-state sensitivity of unity. The dynamics of the system are determined by the first-order transfer function of the sensing element. At time t = 0, the sensing element is suddenly transferred from air at 20 °C to boiling water. One minute later the element is suddenly transferred back to air. Using the data given below, calculate the system dynamic error at the following times: t = 10, 20, 50, 120 and 300 s.

Sensor data

Mass = 5 x 10 ^-2 kg

Surface area = 10 ^-3 m ²

Specific heat = 0.2 J kg ^{-1 °} C ^-1

Heat transfer coefficient for air = 0.2 W m ^-2 °C ^-I

Heat transfer coefficient for water = 1.0 W m ^-2 °C ^-1

Answer rating: 100% (QA)

We have a temperature sensor with mass m 510 2 kg surface area A 110 3 m 2 specific heat capacity c ... View the full answer