# Physics Problem - Total Heat Loss in a House w/60 People

• JoshHull
In summary: AZING! Thanks!In summary, the problem involves calculating the temperature of a house with no heat sources if there are 60 people inside, given a heat loss of 500 W/(Degrees Celsius) and an average power output of 100 W per person. The temperature will rise until there is a temperature difference of 12 degrees Celsius with the outside, but this calculation is complicated by the fact that heat loss increases exponentially with temperature difference.
JoshHull
OK, I have a question that I am trying to do for physics that I just can't figure out. I don't even know how to start it, so any help in getting started would be much appreciated. Here it is:

The total heat loss for a house is 500 W/(Degrees Celsius). The temperature outside the house is 10 (Degrees Celsius). Assume that the average power output for a human body is: 100 W. If there is no heat sources in the house, what will the temperature of the house be if there are 60 people in the house?

If anyone knows how to do the problem, or any ideas of where I should start, that would be great.

JoshHull said:
The total heat loss for a house is 500 W/(Degrees Celsius). The temperature outside the house is 10 (Degrees Celsius). Assume that the average power output for a human body is: 100 W. If there is no heat sources in the house, what will the temperature of the house be if there are 60 people in the house?
This is a confusion statement of the problem. Can you give us the actual wording of the problem?

It appears to be a kind of simplified blackbody radiation problem.

If the total heat loss is 500 Watts/degree C of temperature difference and there are 6000 watts of heat being produced in the house, then the temperature will rise until 6000 watts are being lost. So the temperature will rise until there is a temperature difference of 12 degrees C. with the outside.

The problem is that it is not that simple. The rate of radiation loss increases as the fourth power of the temperature difference.

AM

To start this problem, we can use the formula for heat transfer: Q = U x A x ΔT, where Q is the total heat loss, U is the overall heat transfer coefficient, A is the surface area of the house, and ΔT is the temperature difference between inside and outside the house.

In this case, we know that Q = 500 W/(Degrees Celsius), U is unknown, A is the surface area of the house, and ΔT = (Tinside - 10). We also know that there are 60 people in the house, each producing an average power output of 100 W.

To find the overall heat transfer coefficient (U), we can use the formula: U = 1/Rtotal, where Rtotal is the total thermal resistance of the house. The thermal resistance can be calculated by adding the thermal resistance of each component of the house (walls, windows, roof, etc.).

Once we have the value of U, we can plug it into the formula Q = U x A x ΔT to solve for Tinside.

I hope this helps you get started on the problem. Let me know if you need any further clarification. Good luck!

## 1. What is the formula for calculating total heat loss in a house with 60 people?

The formula for calculating total heat loss in a house with 60 people is Q = U x A x (Tin - Tout), where Q is the heat loss in watts, U is the overall heat transfer coefficient, A is the total surface area of the house, Tin is the indoor temperature, and Tout is the outdoor temperature.

## 2. How does the number of people in a house affect total heat loss?

The number of people in a house can affect total heat loss in several ways. First, the body heat produced by 60 people will contribute to the overall heat load in the house. Second, more people in the house means more breathing, cooking, and other activities that generate moisture and heat, which can increase the humidity and temperature inside the house and result in higher heat loss.

## 3. What are the main factors that contribute to total heat loss in a house?

The main factors that contribute to total heat loss in a house include the insulation of the walls, floors, and ceilings, the size and number of windows, the efficiency of the heating system, and the outdoor temperature and weather conditions.

## 4. How can total heat loss be reduced in a house with 60 people?

To reduce total heat loss in a house with 60 people, you can improve insulation by adding more insulation to walls and attics, seal air leaks around windows and doors, upgrade to energy-efficient windows, use a programmable thermostat to regulate indoor temperature, and ensure that the heating system is properly maintained and functioning efficiently.

## 5. What is the impact of total heat loss in a house with 60 people on energy costs?

Total heat loss in a house with 60 people can significantly impact energy costs. The higher the heat loss, the more energy is required to maintain a comfortable indoor temperature, resulting in higher heating bills. Reducing heat loss through proper insulation and energy-efficient measures can help lower energy costs in the long run.

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