A computer chip with a mass of 50 g, made of copper, experiences an electrical work input of 10-W. The chip is insulated. Initially, the chip has a temperature of 20oC. What is the temperature of the chip after one minute of operation?
Given: Cu; m = 50 g = 0.050 kg; W?= -10 W = -0.010 kW; T1 = 20oC; t = 1 min = 60 s
Assume: Q = 0 (insulated); ?KE = ?PE = 0
What will be an ideal response?
Solution: This is a closed system. Therefore, beginning with the First Law for closed systems, the First Law can be reduced to
W = m (u1 – u2)
In one minute, the total work is W = W?t = (-0.01 kW) (60 s) = -0.60 kJ
Treat the copper as an incompressible substance with constant specific heats: c = 0.385 kJ/kg-K
W = m c (T1 – T2)
Solving, T2 = 51.2oC
Clearly, heat must be transferred away from the chip, or the temperature would quickly rise to the point of damaging/melting the chip.
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