# How Much Does Cooling Cost on a Hot Day with a 5-Ton AC?

• xmonsterx
In summary: You have to find the COP of this refrigerator. Do you know how to determine the COP of a Carnot refrigerator operating between 20C (Tc) and 40C (Th)? (COP = Qc/W). Take 15% of that. (I get 2.2 for the COP of this machine).
xmonsterx

## Homework Statement

PROBLEM:
Refrigeration units can be rated in "tons". A 1-ton air conditioning system can remove sufficient energy to freeze 1 British ton (2000pounds) = 909 kg) of 0 degree C water into 0 degree C ice in one 24-h day.

QUESTION:
If, on a 40 degree C day, the interior of a house is maintained at 20 degree C by the continuous operation of a 5-ton air conditioning system, how much does this cooling cost the homeowner per hour? Assume the work done by the refrigeration unit is powered by electricity that costs $0.10 per kWh and that the unit's coefficient of performance is 15% that of an ideal refrigerator. 1 kWh= 3.60 times 10^6 J. PLEASE GIVE THE ANSWER IN$/hr !

COP = Q_L / W

## The Attempt at a Solution

COP = (40 +273) / W ?

xmonsterx said:

## Homework Statement

PROBLEM:
Refrigeration units can be rated in "tons". A 1-ton air conditioning system can remove sufficient energy to freeze 1 British ton (2000pounds) = 909 kg) of 0 degree C water into 0 degree C ice in one 24-h day.

QUESTION:
If, on a 40 degree C day, the interior of a house is maintained at 20 degree C by the continuous operation of a 5-ton air conditioning system, how much does this cooling cost the homeowner per hour? Assume the work done by the refrigeration unit is powered by electricity that costs $0.10 per kWh and that the unit's coefficient of performance is 15% that of an ideal refrigerator. 1 kWh= 3.60 times 10^6 J. PLEASE GIVE THE ANSWER IN$/hr !

COP = Q_L / W

## The Attempt at a Solution

COP = (40 +273) / W ?

First you have to find how much heat in joules that you have to remove in an hour. (Hint: how much heat does one have to remove from 909 kg of water at 0 C to turn it into ice at 0C?)

Then you have to determine the COP of the air conditioner to determine how much work must be performed to run it for one hour (in Joules and then KwH).

AM

Andrew Mason said:
First you have to find how much heat in joules that you have to remove in an hour. (Hint: how much heat does one have to remove from 909 kg of water at 0 C to turn it into ice at 0C?)

Then you have to determine the COP of the air conditioner to determine how much work must be performed to run it for one hour (in Joules and then KwH).

AM

i don't know what formula to use to find how much heat is removed in an hour. I need additional help/ hints. thanks

xmonsterx said:
i don't know what formula to use to find how much heat is removed in an hour. I need additional help/ hints. thanks
You need to use the heat of fusion of water, which s 333.55 kJ/kg.

AM

Andrew Mason said:
You need to use the heat of fusion of water, which s 333.55 kJ/kg.

AM

wait.. heat of fusion which is Lf = mL = 333.55 ... how does this help me solve for the answer?

what if i use deltaQ = mCdeltaT ?

delta Q = 909kg * 1cal/g C * ((40+273)-(20+273)) ??

does this look right? or am i totally off?

xmonsterx said:
wait.. heat of fusion which is Lf = mL = 333.55 ... how does this help me solve for the answer?

what if i use deltaQ = mCdeltaT ?

delta Q = 909kg * 1cal/g C * ((40+273)-(20+273)) ??

does this look right? or am i totally off?
You cannot use $\Delta Q = mC\Delta T$ because there is no change in temperature. Only a change of state. So you have to use:

$$\Delta Q = mL_f$$ where $L_f$ is the heat of fusion of water.

AM

Andrew Mason said:
You cannot use $\Delta Q = mC\Delta T$ because there is no change in temperature. Only a change of state. So you have to use:

$$\Delta Q = mL_f$$ where $L_f$ is the heat of fusion of water.

AM

ok so...
delta Q = (909kg) * (333.55) = 3.0*10^5

so then do i plug this number in this equation --> COP= Q_L / W --> COP = Q_L / Q_H -Q_L ??

am i on the correct path??

xmonsterx said:
ok so...
delta Q = (909kg) * (333.55) = 3.0*10^5

so then do i plug this number in this equation --> COP= Q_L / W --> COP = Q_L / Q_H -Q_L ??

am i on the correct path??
You have to find the COP of this refrigerator. Do you know how to determine the COP of a Carnot refrigerator operating between 20C (Tc) and 40C (Th)? (COP = Qc/W). Take 15% of that. (I get 2.2 for the COP of this machine).

AM

## 1. How does a refrigerator keep food cold?

A refrigerator uses a compressor, coils, and refrigerant to remove heat from inside and expel it outside. This creates a continuous cycle of cooling and maintains a cold temperature inside the refrigerator.

## 2. How often should I clean my refrigerator?

It is recommended to clean your refrigerator at least once every 3 months. However, if you notice any spills or buildup, it is best to clean it immediately to prevent bacteria growth.

## 3. Can I store hot food in the refrigerator?

No, it is not safe to store hot food in the refrigerator. The hot temperature can raise the overall temperature inside the refrigerator, potentially causing bacteria to grow and spoil other foods.

## 4. Why is there water collecting at the bottom of my refrigerator?

This is most likely due to a clogged or frozen drain tube. The drain tube is responsible for directing excess water from the defrost cycle to the drip pan. If it is clogged or frozen, the water will collect at the bottom of the refrigerator. It is important to clean or thaw the drain tube to prevent any damage to the refrigerator.

## 5. How do I know if my refrigerator is running efficiently?

You can check the energy efficiency of your refrigerator by looking for an Energy Star label. This means that the refrigerator meets energy efficiency guidelines set by the Environmental Protection Agency. You can also monitor the temperature inside the refrigerator and make sure the door seals are tight to prevent cold air from escaping.

• Introductory Physics Homework Help
Replies
11
Views
2K
• Engineering and Comp Sci Homework Help
Replies
12
Views
4K
• Introductory Physics Homework Help
Replies
6
Views
7K
• Introductory Physics Homework Help
Replies
7
Views
5K
• Engineering and Comp Sci Homework Help
Replies
2
Views
2K
• Engineering and Comp Sci Homework Help
Replies
2
Views
2K
• Thermodynamics
Replies
26
Views
9K
• Introductory Physics Homework Help
Replies
2
Views
8K
• Thermodynamics
Replies
2
Views
2K
• Biology and Chemistry Homework Help
Replies
3
Views
3K