Ask question

Ask question

All categories

3 years ago

8

The drinking water needs of an office are met by cooling tab water in a refrigerated water fountain from 23 to 6°C at an average

rate of 10 kg/h. If the COP of this refrigerator is 3.1, the required power input to this refrigerator is
(a) 197W
(b) 612W
(c) 64W
(d) 109W
(e) 403W

2 answers:

Ratling [72]3 years ago

4 0

Answer:

The correct option is;

(c) 64W

Explanation:

Here we have the Coefficient Of Performance, COP given by

$COP = \frac{Q_{cold}}{W} = 3.1$

The heat change from 23° to 6°C for a mass of 10 kg/h which is equivalent to 10/(60×60) kg/s or 2.78 g/s we have

$Q_{cold}$ = m·c·ΔT = 2.78 × 4.18 × (23 - 6) = 197.39 J

Therefore, plugging in the value for $Q_{cold}$ in the COP equation we get;

$COP = \frac{197.39 }{W} = 3.1$ which gives

$W = \frac{197.39 }{3.1} = 63.674 \ J$

Since we were working with mass flow rate then the power input is the same as the work done per second and the power input to the refrigerator = 63.674 J/s ≈ 64 W.

The power input to the refrigerator is approximately 64 W.

-BARSIC- [3]3 years ago

3 0

Answer:

Win = 64 W ... Option C

Explanation:

Given:-

- The water is cooled in the refrigerator with delta temperature, ΔT=(23 - 6 )

- The flow rate of the refrigerated water is flow ( m ) = 10 kg/h

- The COP of the refrigerator is = 3.1:

Find:-

the required power input to this refrigerator is

Solution:-

- The COP - The coefficient of performance of a refrigerator is a quantity that defines the efficiency of the system. The COP is given as:

COP = QL / Win

Where,

QL : The rate of heat loss

Win : The input power required

- The rate of heat loss can be determined from first law of thermodynamics.

Qin - Wout = flow (m)*c*ΔT

Where,

Qin = - QL ... Heat lost.

c : The heat capacity of water = 4,200 J / kg°C

- There is no work being done on the system so, Wout = 0

-QL = flow (m)*c*ΔT

-QL = ( 10 / 3600 )*4200*( 6 - 23 )

QL = 198.33 W

- The required power input ( Qin ) would be:

Win = QL / COP

Win = 198.33 / 3.1

= 63.97 W ≈ 64 W

You might be interested in

100 g of Ice at -10°C is added into a

Andrei [34K]

Answer:

The mass of the juice responsible for melting the ice is 949.043 grams.

Explanation:

By the First Law of Thermodynamics, we understand that juice releases heat to the ice, which turns into water under the assumption that interactions between the ice-juice system and surroundings are negligible and energy processes are done in steady-state. Since juice is done with water, its specific heat will be taken as of the water. The process is described by the following formula:

$m_{i} \cdot [c_{i}\cdot (T_{1}-T_{2}) - L_{f} + c_{w}\cdot (T_{2}-T_{3})] + m_{w} \cdot c_{w}\cdot (T_{4}-T_{3}) = 0$ (1)

Where:

$m_{i}$ - Mass of ice, in grams.

$m_{w}$ - Mass of the juice, in grams.

$c_{i}$ - Specific heat of ice, in joules per gram-degree Celsius.

$c_{w}$ - Specific heat of water, in joules per gram-degree Celsius.

$L_{f}$ - Latent heat of fusion, in joules per gram.

$T_{1}$ - Initial temperature of ice, in degrees Celsius.

$T_{2}$ - Melting point of water, in degrees Celsius.

$T_{3}$ - Final temperature of the ice-juice system, in degrees Celsius.

$T_{4}$ - Initial temperature of the juice, in degrees Celsius.

If we know that $m_{i} = 100\,g$ , $c_{i} = 2.090\,\frac{J}{g\cdot ^{\circ}C}$ , $c_{w} = 4.18\,\frac{J}{g\cdot ^{\circ}C}$ , $L_{f} = 334\,\frac{J}{g}$ , $T_{1} = -10\,^{\circ}C$ , $T_{2} = 0\,^{\circ}C$ , $T_{3} = 10\,^{\circ}C$ and $T_{4} = 20\,^{\circ}C$ , then the mass of the juice is:

$m_{w} = \frac{m_{i}\cdot [c_{i}\cdot (T_{1}-T_{2}) - L_{f} + c_{w}\cdot (T_{2}-T_{3})]}{c_{w} \cdot (T_{3}-T_{4})}$

$m_{w} = \frac{(100\,g)\cdot \left[\left(2.090\,\frac{J}{g\cdot ^{\circ}C} \right)\cdot (-10\,^{\circ}C) - 334\,\frac{J}{g} +\left(4.18\,\frac{J}{g\cdot ^{\circ}C} \right)\cdot (-10\,^{\circ}C) \right]}{\left(4.180\,\frac{J}{g\cdot ^{\circ}C} \right)\cdot (-10\,^{\circ}C)}$

$m_{w} = 949.043\,g$

The mass of the juice responsible for melting the ice is 949.043 grams.

5 0

3 years ago

When white light is incident on a prism, which one of the resulting color components will have the lowest index of refraction?

soldi70 [24.7K]

Blue has the lowest index of refraction

3 0

3 years ago

Read 2 more answers

Arrange the objects in order from least to greatest potential energy. Assume that gravity is constant. (Use PE = m × g × h.)

yawa3891 [41]

Answer:The objects in order from least to greatest potential energy:

3<1<4<2

Explanation:

1. Potential energy of a 15-kilogram stone found at a height of 3 meters:

$mgh=15 kg\times 9.8 m/s^2\times 3 m=441 J$

2. Potential energy 10 kilograms of water stored at a height of 9 meters:

$mgh=10 kg\times 9.8 m/s^2\times 9 m=882 J$

3. Potential energy 1-kilogram ball located 20 meters in the air:

$mgh=1 kg\times 9.8 m/s^2\times 20 m=196 J$

4. Potential energy box of books weighing 25 kilograms placed on a shelf 2 meters high:

$mgh=25 kg\times 9.8 m/s^2\times 2 m=490 J$

The objects in order from least to greatest potential energy:

3<1<4<2

8 0

3 years ago

Read 2 more answers

1200 meters is less than 1 kilometer

SashulF [63]

<span>1200 meters is less than 1 kilometer
</span>is false

4 0

4 years ago

Read 2 more answers

Which law describes the magnetic field in a nonlinear wire? A. Faraday's law B. Gauss's law C. Ohm's law D. Ampère's law

Korolek [52]

Answer:

B. Gauss’s law

Explanation:

Gauss’s law is defined as the act of thinking something carefully, careful thought; meditation; deliberation. consideration acts like filter on the information a person receives, because it allows them to contemplate the implications of something before acting on it.

hope this helped!

7 0

3 years ago