From Robert Balmer\'s Modern Engineering Thermodynamics, chapter 9, problem 29:

Question

From Robert Balmer's Modern Engineering Thermodynamics, chapter 9, problem 29:

A slide projector contains a 500 W light bulb cooled by an internal fan that blows room air across the bulb at a rate of 1.00 kg/min. If the equilibrium surface temperature of the bulb is 350°C and the inlet temperature (the room air) is at 20.0°C, then determine:

(a) the outlet temperature of the cooling air and
(b) the rate of entropy production in the air passing through the projector.

Assume the air is an ideal gas with constant specific heats and that no work is performed.

Help would be appreciated. Thank you.

Explanation / Answer

(a) Applying first law at the inlet and outlet of cooling air,

Q-W = Hout - Hin = mCp(T2 - T1)

We have Q = 500 W, W = 0, m = 1 kg/min = 0.0167 kg/s, Cp = 1005 J/kg-K, T1 = 20 deg C.

Putting values, we get T2 = 49.9 deg C 50 deg C.

(b) Rate of entropy production = m(s2 - s1) - Q/T

From tables of ideal gas properties for air, s1 = 1668.02 J/kg-K, and s2 = 1766.9 J/kg-K

So, Rate of entropy production = 0.0167(1766.9 - 1668.02) - 500/(273+350)

= 0.8487 J/s-K.

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