Achip that is of length l = 5 mm on a side and thickness t = 1 mm is encased in a ceramic substrate, and its exposed surface is convectively cooled by a dielectric liquid for which h = 150 w/m^2
⋅
k and t = 20
o
c. in the off-mode the chip is in thermal equilibrium with the coolant (t
i
= t
[infinity]
) when the chip is energized, however, its temperature increases until a new steeds state is established. for purposes of analysis. the energized chip is characterized by uniform volumetric heating with q = 9
×
10
6
w/m
3
.

a) assuming an infinite contact resistance between the chip and substrate and negligible conduction resistance within the chip, determine the steady-state chip temperature t
f
.
b) following activation of the chip, how long does it take to come within 1
o
c of this temperature? the chip density and specific heat are
rho
= 2000 kg/m
3
and c = 700 j/kg
⋅
k, respectively.