1. Mathematics and Home Insulation
Question
If it is about 27°F outside with no wind, how much is our heat bill affected if we set the thermostat to 84°F instead of 55°F ?
CHOICE A – Our heat bill is doubled
CHOICE B – Our heat bill increases $200/mo
CHOICE C – Our heat bill increases 50%
CHOICE D – Our heat bill is tripled
Can we use mathematics to justify our answer?

2. Answer: CHOICE A – Our heat bill is doubled.
The reason we can state this is due to laws of heat transfer, and some mathematics. In the equation below, Q represents the power, i.e. the energy used per time.
Raising the thermostat from 55°F to 84°F approximately doubles the temperature difference ΔT between inside and outside in degrees C. When ΔT doubles, Q doubles since K, A, and x are constant!
For More Info on The Mathematics of Heat Transfer See The Mathematics of Heat Transfer