How to Determine the Minimum Heat Extraction from a Furnace?

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In summary, the conversation discusses the heating of a house by a furnace and considers the use of a third heat reservoir to reduce the amount of heat needed from the furnace. Given the temperatures of the furnace, house, and surroundings, and the amount of heat required to maintain the house's temperature, the minimum amount of heat that must be extracted from the furnace is determined using Carnot's principle. The problem statement is not clear and may contain some mistakes.
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Homework Statement


Consider the heating of a house by a furnace, which serves as a heat-source reservoir at a
high temperature TF. The house acts as a heat sink at temperature T, and heat |Q| must be
added to the house to maintain this temperature. Heat |Q| can of course be transferred
directly from the furnace to the house, as is common practice. However, a third heat
reservoir is readily available, namely, the surroundings at temperature T ., which can
serve as another heat source, thus reducing the heat required from the furnace. Given that
TF = 810 K, T = 295 K, Tσ = 265 K. and |Q| = 1,000 kJ, determine the minimum amount
of heat |QF| which must be extracted from the heat-source reservoir (furnace) at TF . No
other sources of energy are available.


Homework Equations





The Attempt at a Solution


I am not sure if the way I am interpreting the question is right. There are some seemingly obvious mistakes, such as saying that the outside temperature helps reduce the amount of heat needed by the furnace.
 

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  • #2
When a refrigerator works, heat is transferred from its colder internals to its warmer surroundings, so such transfer is not impossible.
 
  • #3
I agree the problem statement isn't at all clear.

It talks about the heat needed to "maintain" the temperature of the house. Normally that would suggest we are talking about power flows (eg to maintain a temperature the power flowing into and out of the house must sum to zero). However it states that the "heat" required is "1,000 kJ" which is energy not power.

It sounds like they are trying to get you to apply Carnot.
 
  • #4
Yes, did I apply carnot correctly?
 
  • #5
This is not true. The outside temperature will actually cause heat loss from the house, so the furnace will need to produce more heat to maintain the desired temperature inside. Also, the given temperatures do not make sense, as the outside temperature (T) is higher than the surroundings temperature (Tσ).

Assuming that the question is asking for the minimum amount of heat that needs to be extracted from the furnace in order to maintain the desired temperature inside the house, we can use the First Law of Thermodynamics:

ΔU = Q - W

Where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system. In this case, we can assume that the work done is negligible.

Therefore, we can rearrange the equation to solve for Q:

Q = ΔU

We know that the only source of energy is the furnace at TF, so the change in internal energy (ΔU) will be equal to the amount of heat extracted from the furnace (|QF|).

Therefore, we can say that the minimum amount of heat required from the furnace is:

|QF| = ΔU = T(TF - T)

Plugging in the given temperatures, we get:

|QF| = 295(810-295) = 336,175 kJ

However, this does not take into account any heat loss from the house due to outside temperature. In reality, the furnace would need to produce more heat to compensate for this heat loss, so the minimum amount of heat required from the furnace would actually be higher than this calculated value.
 

FAQ: How to Determine the Minimum Heat Extraction from a Furnace?

What is a furnace?

A furnace is a heating system that uses heat energy to warm up a space, such as a house or building. It typically runs on natural gas, propane, or electricity.

How does a furnace work?

A furnace works by taking in cold air from the house, heating it up through a combustion process, and then blowing the warm air back into the house through a system of ducts and vents.

What are the different types of furnaces?

There are three main types of furnaces: gas, electric, and oil. Gas furnaces are the most common and use natural gas or propane as fuel. Electric furnaces use electricity to heat up coils, and oil furnaces use oil as fuel.

How do I know what size furnace I need for my house?

The size of the furnace you need depends on the size of your house and your climate. A professional HVAC technician can help determine the appropriate size for your home by conducting a heat load calculation.

How often should I replace my furnace?

The average lifespan of a furnace is about 15-20 years. However, its lifespan can vary depending on usage, maintenance, and quality of the furnace. It is recommended to replace your furnace every 15-20 years to ensure optimal efficiency and performance.

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