What Is the Breakeven Point for Upgrading to Thicker Insulation Walls?

[sdoyle1]

Homework Statement

I'm not sure if this problem should go here.. it's a bit of math and a bit of physics. I know that the concepts should be simple but I don't really know where to start.. Here's the question:
a) Determine the breakeven point for heating oil in dollars per gallon – the point where it would be worth enduring the cost of going to 2 x6 walls from 2 x4 walls in a house of 2000 square feet. We are looking at a payback of 3 years as interest rates have risen to 12 percent and with the high unemployment rate there is little cash around. State any assumptions made in addition to those given.

Homework Equations

There were a number of assumptions given to us:
Assume all heat loss is thru walls (no windows, doors etc.) No effect via basement or roof.
Assume 10 studs per 100 sq feet.
Assume all heat movement is due to conduction, no radiation or convection.
Assume oil initially at $4.00 per liter, fuel oil number 2 averages 140,000 Btu per Gallon(US) and a furnace efficiency of 92%
Median season length of 7 months.
Median outside temperature of 27 degrees C
Indoor temperature kept at 70 degrees

The Attempt at a Solution

I am assuming that you need to use R=deltaT/Q but I'm really not sure. I don't want someone to do the question for me... just kind of guide me in the right direction :)

 

[anathema]

Thank you for posting your question. It seems like you have a good understanding of the basic concepts involved in this problem. The equation R=deltaT/Q is indeed relevant here, as it relates to the thermal resistance of a material.

To determine the breakeven point for heating oil in dollars per gallon, we first need to calculate the cost of heating the house with 2x4 walls and with 2x6 walls. This will give us the difference in cost, which we can then compare to the cost of upgrading to 2x6 walls.

To calculate the cost of heating with 2x4 walls, we need to determine the heat loss through the walls. This can be done using the equation Q=U*A*deltaT, where Q is the heat loss, U is the overall thermal conductance of the walls, A is the area of the walls, and deltaT is the temperature difference between the inside and outside of the house. We can assume that the temperature difference is constant at 43 degrees C (70-27=43). We can also calculate the area of the walls using the given information of 10 studs per 100 sq feet.

Next, we need to determine the cost of heating with 2x6 walls. This can be done in the same way as above, but with a different value for U. We can assume that the U value for 2x6 walls is lower than that for 2x4 walls, as the thicker walls will have a higher thermal resistance.

Once we have calculated the cost of heating with both types of walls, we can compare them to the cost of upgrading to 2x6 walls. If the cost difference is less than the cost of upgrading, then it would be worth enduring the cost of the upgrade.

I hope this helps guide you in the right direction. It's always important to make assumptions clear in any problem, as they can greatly affect the outcome. Good luck with your calculations!