Applying the Exergy Balance: Closed SystemsAs

QUESTION:

As shown in Fig. P7.44, a silicon chip measuring 5 mm on a side and 1 mm in thickness is embedded in a ceramic substrate. At steady state, the chip has an electrical power input of 0.225 W. The top surface of the chip is exposed to a coolant whose temperature is \(20^{\circ} \mathrm{C}\). The heat transfer coefficient for convection between the chip and the coolant is 150 \(\mathrm{~W} / \mathrm{m}^2 \cdot \mathrm{K}\). Heat transfer by conduction between the chip and the substrate is negligible. Determine (a) the surface temperature of the chip, in \({ }^{\circ} \mathrm{C}\), and (b) the rate of exergy destruction within the chip, in W. What causes the exergy destruction in this case? Let \(T_0\) = 293 K.