Energy problem dealing with heat extracted from cold air

In summary, the heat pump requires 385 W of electrical power to deliver 2410 J of heat per second to the house. To extract this heat from the cold air outside, Q1 must be removed at temperature T1 while Q2 is added at temperature T2. For a reversible process, the equation \frac{Q_1}{T_1}=\frac{Q_2}{T_2} can be used, where T1<T2 and Q2>Q1. The difference between Q2 and Q1 is the work done by the heat pump.
  • #1
astru025
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Homework Statement



A heat pump requires 385 W of electrical power to deliver heat to your house at a rate of 2410 J per second. How many joules of energy are extracted from the cold air outside each second?


Homework Equations



COP= Qc / W . This was the only equation I could find.

The Attempt at a Solution


Any help would be nice! I tried the above equation but I turned out to be incorrect.
 
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  • #2
use this and find out the ans...
 
  • #3
What do you think happens to the electrical energy used by the pump?
 
  • #4
This is the same as an air conditioner that is cooling the outside and rejecting the heat to the inside. If the heat pump operates reversibly, then Q1 is removed from the outside at temperature T1, and Q2 is added to the inside at temperature T2. For a reversible process, such that ΔS of the surroundings = 0, [itex]\frac{Q_1}{T_1}=\frac{Q_2}{T_2}[/itex]. Since T1<T2, Q2>Q1. The difference between Q2 and Q1 is the work done by the heat pump.
 
  • #5


I would approach this problem by first looking at the definition of a heat pump. A heat pump is a device that transfers heat from a colder area to a warmer area, using mechanical or electrical energy. In this case, the heat pump is using 385 W of electrical power to deliver 2410 J of heat per second to the house. This means that the heat pump has a coefficient of performance (COP) of 2410 J/385 W = 6.26.

Now, to find the amount of energy extracted from the cold air outside each second, we can use the equation Qc = Qh - W, where Qc is the energy extracted from the cold air, Qh is the heat delivered to the house, and W is the electrical power used by the heat pump. Plugging in the values given, we get Qc = 2410 J/s - 385 W = 2025 J/s. This means that 2025 J of energy is extracted from the cold air outside each second.

It is important to note that this calculation assumes ideal conditions and does not take into account any losses or inefficiencies in the heat pump system. In reality, the amount of energy extracted from the cold air may be slightly lower. Additionally, the specific temperature and humidity of the cold air outside can also affect the amount of energy that can be extracted.
 

Related to Energy problem dealing with heat extracted from cold air

1. How does extracting heat from cold air help with the energy problem?

Extracting heat from cold air can help with the energy problem by providing a renewable source of energy. Cold air is constantly present in the environment, making it an easily accessible and abundant source of energy. By extracting heat from the cold air, we can convert it into usable energy to power our homes, businesses, and vehicles.

2. What technologies are used to extract heat from cold air?

There are several technologies that can be used to extract heat from cold air. Some common methods include air source heat pumps, geothermal heat pumps, and absorption heat pumps. These technologies use different mechanisms, such as compressors and refrigerants, to extract heat from the cold air and transfer it to a usable form of energy.

3. Is extracting heat from cold air a sustainable solution?

Yes, extracting heat from cold air is considered a sustainable solution for the energy problem. As mentioned before, cold air is a renewable resource that is constantly replenished by the natural processes of the environment. By using this resource, we can reduce our dependence on non-renewable sources of energy, such as fossil fuels, which contribute to climate change and other environmental issues.

4. Can extracting heat from cold air be used in all climates?

While extracting heat from cold air is most effective in colder climates, it can still be used in all climates. In warmer climates, the temperature difference between the cold air and the desired temperature for energy use may be smaller, making the process less efficient. However, advancements in technology have made it possible to extract heat even from relatively warm air.

5. Are there any drawbacks to extracting heat from cold air?

One potential drawback of extracting heat from cold air is its initial cost. The installation and maintenance of the necessary technologies can be expensive. Additionally, the efficiency of these technologies may decrease in extreme temperatures, leading to a decrease in energy output. However, the long-term benefits of using a renewable source of energy often outweigh these drawbacks.

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