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(a) A freezer maintains an interior temperature inside of −12.0°C and has a coefficient of performance of 3.00. The freezer sits in a room with a temperature of 19.0°C. The freezer is able to completely convert 26.0 g of liquid water at 19.0°C to ice at −12.0°C in one minute. What input power (in watts) does the freezer require? (The specific heat of liquid water is 4.186 J/(g · °C), the specific heat of ice is 2.090 J/(g · °C), and the latent heat of fusion of water is 334 J/g.)

(b) What If? In reality, only part of the power consumption of a freezer is used to make ice. The remainder is used to maintain the temperature of the rest of the freezer. Suppose, however, that 100% of a freezer's typical power consumption of 160 W is available to make ice. The freezer has the same coefficient of performance as given above. How many grams per minute of water at 19.0°C could this freezer convert to ice at −12.0°C? g/min

The heat required to free the water at 17°c is that required to reduce it to water at 0°c plus that to convert it to ice at 0°c plus that required to get it to ice at -12°c.

Note that in the conversion process mass is constant.

Hence the heat extracted is defined as mass ×specific heat capacity × temperature change.

But on conversion from water to ice at 0°c the heat extracted is mass × latent heat of fusion.

Putting all together we have :

26 ×4.186 ×(0-19) -26 ×334 + 26 × 2.090× (-12-0)

=2067.884+8684+652.08=9988.16J

This is the output power

From performance formula;

Coefficient of performance=output power /input power

Input power = output power / coefficient of performance

Input power=9988.16J/3 =3329.39j

In watt we divide by 60

3329.39/60= 55.49W

Note the negative sign is just an indication that heat is been lost from the system.

B. Let's calculate Energy per unit mass of the process

9988.16J/26 =384.16J/g

Power consumption is 160w

This is the input power of the system

160 W is available to make ice.

This means 160 ×60 J is the energy available to make ice since the whole process takes 60s.

That energy =9600J

But the output energy per unit mass is 384.16J/g.

Hence the required mass for 9600J is

9600/384.16= 24.99g

Approximately 25g

priyankatutor priyankatutor · Answer 2 · 2021-12-11T13:35:04+01:00

Freezer requires 55,49 W of input of energy and the 25 g/ min of water at 19.0°C, this freezer convert to ice at −12.0°C.

(A)

Since, mass is constant.

Thus,

[tex]\bold {Q = mc\Delta T}[/tex]...........1

But on conversion from water to ice at 0°c

Q = m x Lf...........2

From equation 1 and 2,

26 ×4.186 ×(0-19) -26 ×334 + 26 × 2.090× (-12-0)

=2067.884 + 8684 + 652.08 = 9988.16 J

From performance formula;

[tex]\bold {Pi = \dfrac {Po} {CoP}}[/tex]

Where,

Pi - power input

Po - Power output

CoP - Coefficient of power

[tex]\bold { Pi =\dfrac {9988.16\ J}{3} = 3329.39 J = 55.49 W}[/tex]

(B)

Since, the negative sign indicate the lost of heat from the system.

Calculate Energy per unit mass of the given process

9988.16J/26 =384.16 J/g

Power consumption = 160 W

Since, the whole process takes 60s.

160 ×60 J = 9600 J

But the output energy per unit mass is 384.16J/g.

Hence the required mass for 9600J,

9600/384.16= 24.99g = 25 g/min

Therefore, freezer requires 55,49 W of input of energy and the 25 g/ min of water at 19.0°C, this freezer convert to ice at −12.0°C.

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