A transistor has a mass m = 1.5 grams, and specific heat, cp = 510 J/kg.K, and thermal conductivity, k = 15 W/m.K. It has a surface area, AS = 6.75 cm^2 and convection coefficient, h = 12 W/m^2.K.
After operating at a steady temperature for several hours, the transistor is switched off at time, t = 0, with an initial temperature, Ti = 100°C and the ambient air temperature, T∞ = 40°C.
a) What was the steady-state power dissipation of the transistor, P, immediately prior to switching off.
b) If the characteristic length is LC = 2.5 mm, determine the Biot number. Is the lumped capacitance model a reasonable choice here? Why or why not?
c) Using conservation of energy formulate a differential equation for temperature as a function of time.
d) What is the time constant of the above first-order equation?
e) Determine the temperature reached after 1.0 s, 10 s, and 100 s.