Question

A certain brand of freezer is advertised to use 685 kW · h of energy per year. (a) Assuming the freezer operates for 4.5 hours each day, how much power does it require while operating? W (b) If the freezer keeps its interior at a temperature of −9.5°C in a 21.4°C room, what is its theoretical maximum performance coefficient? (c) What is the theoretical maximum amount of ice this freezer could make in an hour, starting with water at 21.4°C?

Answer 1

Hello let's solve this problem:

For A

we have that

This is the W spent each hour it functions. Meaning that each day it will spend:

ANSWER FOR B (you can just put 351.9 W in 4.5 hours)

Now for B

The greatest performance coefficient is that of a Carnot's machine. And the formula to determine this for cooling machines is:

Before solving to find the coefficient all temperatures must be converted into K

K=^oC+273.15

Then we have that:

ANSWER FOR B

For C

Let's recall that the specific heat and the latent heat for water is:

Cw is the same value for Kelvin degrees.

We have two different phases.

First we have to change the temperature of water to 0 C this Q1.

Then we have to convert this unknown mass of water into ice, this is Q2.

But there is a total heat used in both fases:

We can find this total Q:

We spend 78.2 W an hour, and an hour has 3600 seconds:

Now to find the mass of water converted into ice we return to

Remember

Then

We now simply clear Mw:

We proceed to find delta T which will have a negative sign, because the temperature is diminishing.

The temperature of water in Kelvin is 295.55

We now have all the data and after making the substitution in:

We will find that:

Good luck