Entropy in the Real World: Refrigerators — Question 7

Question 7

An open refrigerator warms the insulated room that contains it

An operating refrigerator stands with its door open in an insulated room. It receives 200 W of electrical power from outside and has instantaneous cooling rate 600 W. Both its cold and warm heat exchangers lie inside the room. The combined room and apparatus heat capacity is 10000 J/K, with negligible other energy storage.

1. Find heat rejection rate and net room heating rate.

2. Find the initial temperature-rise rate and the time for a 1.00 K rise if power and heat capacity remain constant. Would increasing cooling coefficient at the same electrical power change that net heating?

Question 7 - Solution

An open refrigerator warms the insulated room that contains it

(a) Method and calculation

$$\dot Q_h=\dot Q_c+\dot W=600+200=800\,\mathrm W.$$$$\dot Q_{\mathrm{net,room}}=\dot Q_h-\dot Q_c=200\,\mathrm W.$$

(b) Interpretation and further calculation

$$C\frac{dT}{dt}=200\ \Rightarrow\frac{dT}{dt}=.0200\,\mathrm{K/s},\quad t=\frac{C(1.00)}{200}=50.0\,\mathrm s.$$$$\dot Q_h-\dot Q_c=\dot W\quad\text{for any cyclic coefficient}.$$Internal heat relocation cancels at the room boundary; the external electrical input remains.

Physical check

The conclusion depends on both heat exchangers being inside the same insulated boundary.