Question

A 20 centimeter long copper wire sensor is designed to alert if the temperature elevates beyond a safe region causing the wire to make contact with the wall, 1.5 mm away at 25 C. What temperature (in K) will the copper wire make contact with the wall, setting the sensor off? The thermal coefficient of expansion, α, for copper (Cu) is found to be 16.6 ppm/K (16.6x10-6 /K).

Answer 1

The temperature is 749.8 K

Step-by-step explanation:

Final temperature (T2) = (distance apart/thermal coefficient of expansion×length) + initial temperature

distance apart = 1.5 mm = 1.5/1000 = 0.0015 m

thermal coefficient of expansion for copper = 16.6×10^-6/K

Length of copper = 20 cm = 20/100 = 0.2 m

Initial temperature = 25 °C = 25 + 273 = 298 K

T2 = (0.0015/16.6×10^-6×0.2) + 298 = 451.8 + 298 = 749.8 K