## Related questions with answers

A refrigerator has a coefficient of performance of 2.25, runs on an input of 135 W of electrical power, and keeps its inside compartment at $5^{\circ} \mathrm{C}$. If you put a dozen 1.0-L plastic bottles of water at $31^{\circ} \mathrm{C}$ into this refrigerator, how long will it take for them to be cooled down to $5^{\circ} \mathrm{C}$? (Ignore any heat that leaves the plastic.)

Solutions

VerifiedWe will solve this problem by using the fact that refrigerator takes heat from inside the refrigerator required for lowering temperature of water in bottles from initial temperature (temperature of water bottles when they are placed inside the refrigerator) to final temperature (temperature inside refrigerator that is kept constant).

We are given:

- coefficient of performance of refrigerator $K=2.25$ -electrical power input of refrigerator $P=135 \mathrm{~W}$
- temperature inside the refrigerator $T_r=5^{\circ}$
- volume of each of the water bottle $V=1 \mathrm{~L}$
- number of water bottles placed inside the refrigerator $N=12$ (dozen water bottles)
- initial temperature of water in water bottles $T_{wb}=31^{\circ}$

We need to know to solve this problem:

- specific heat capacity of water $c=4179 \mathrm{~\tfrac{J}{kg \cdot K}}$
- mass density of water $\rho=1000 \mathrm{~\tfrac{kg}{m^3}}$

$COP=\dfrac{Q_{c}}{W}$

draw a picture to help understand the process

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