Calculating the Cheaper Option for Heating Room

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In summary, the given problem involves an oil-filled radiator used to maintain a room temperature of 21C when the outside temperature is 10C. The radiator has a surface area of 1.5 m2, a surface temperature of 70C, and is made of a metal with a thermal conductivity of 80 Wm-1K-1, thermal convection coefficient of 9.5 Wm-2K-1, and emissivity of 0.8. The first question asks for the amount of work done by a heat pump with a coefficient of performance of 9, and the second question asks for the cheaper option between using the radiator and pump for electricity. To solve,
  • #1
pcoppin
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Homework Statement



An oil-filled radiator is used to maintain the temperature of a room at 21C when the outside temperature is 10C. The radiator has a surface area of 1.5 m2, and a surface temperature of 70C. Given that the radiator is made of a metal with a thermal conductivity 80 Wm-1K-1, thermal convection coefficient of 9.5 Wm-2K-1 and an emissivity of 0.8.

Question 1: If it was decided that a heat pump would be a better wat to heat this room, how much work would be done by the pump with a coefficient of performance of 9?

Question 2: If both the radiator and pump were run by electricity, which would be the cheaper option? Why?

Homework Equations



Currently, the rate at which heat is transferred into the room by convection plus radiation from the radiator is equal to the rate at which heat is conducted through the metal.
The Rate of Transfer is 1131.67 W (not sure if this is relevant)

The Attempt at a Solution



Not sure what to do as only given the coefficient of performance as 9.
 
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  • #2
pcoppin said:

Homework Statement



An oil-filled radiator is used to maintain the temperature of a room at 21C when the outside temperature is 10C. The radiator has a surface area of 1.5 m2, and a surface temperature of 70C. Given that the radiator is made of a metal with a thermal conductivity 80 Wm-1K-1, thermal convection coefficient of 9.5 Wm-2K-1 and an emissivity of 0.8.

Question 1: If it was decided that a heat pump would be a better wat to heat this room, how much work would be done by the pump with a coefficient of performance of 9?

Question 2: If both the radiator and pump were run by electricity, which would be the cheaper option? Why?
First, find the rate at which energy is radiated and convected away from the radiator surface. That is the rate of heat output. Then find the rate at which work is done by a heat pump with a COP of 9 that delivers that rate of heat output . Use:

[tex]COP = \dot Q_h/\dot W[/tex]

AM
 
  • #3
I think there is a formula in calculating the total amount of heat are you using. I don't remember. Where can I saw this formula? My suggestion is trying to apply the formula if you find it.
 

1. How do I calculate the cheaper option for heating a room?

To calculate the cheaper option for heating a room, you will need to determine the cost of each heating method (such as electric, gas, or wood) and compare them. This can be done by finding the cost per unit of energy for each method and multiplying it by the amount of energy needed to heat the room. Whichever method has the lowest cost is the cheaper option.

2. What factors should I consider when calculating the cheaper option for heating a room?

Some factors to consider when calculating the cheaper option for heating a room include the cost of the heating method, the energy efficiency of the heating system, the size and insulation of the room, and the climate of the location.

3. Is it more cost-effective to use a space heater or central heating for heating a room?

This depends on various factors such as the size of the room, the energy efficiency of the space heater, and the cost of electricity in your area. In general, central heating is more cost-effective for larger rooms, while a space heater may be more cost-effective for smaller rooms or if you only need to heat a specific area.

4. How can I make my heating system more energy-efficient?

To make your heating system more energy-efficient, you can ensure that your home is well-insulated, regularly maintain your heating system, and consider investing in a programmable thermostat. You can also reduce your energy usage by setting the thermostat to a lower temperature and using natural sunlight to warm up the room during the day.

5. Are there any government programs or incentives to help with the cost of heating a room?

Yes, there are various government programs and incentives available to help with the cost of heating a room. These may include tax credits for energy-efficient heating systems, rebates for upgrading to more efficient heating systems, and assistance programs for low-income households. It is recommended to research and inquire about these programs in your area.

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