Answer
a) 319/month
b) 37.58/month
Work Step by Step
a) We know that the heat loss through the roof will still be 1839 Btu/h. We can find the new heat loss through the walls by using the change in surface area of the walls:
$=5963\times (\frac{1506-125}{1506})=5468 \ Btu/h$
Now, we find the heat loss through the windows:
$=(\frac{1}{.9}\times(2.5)(5)(10 \ windows)(50^{\circ}F)=6944 \ Btu/h$
Thus, we find:
$=(6944+1839+5468)(24 h/day)(30day/month)=10.25 MBtu$
This corresponds to a cost of 356.43 dollars.
However, we must also considered the energy that comes through the south windows, which we are asked to find in part b, anyways. Thus, we obtain:
$=(30)(24)(30)(2.5)(5)(4\ windows)=1.08\ MBtu$
This corresponds to a cost of $\fbox{37.58 dollars per month}$
This means that the answer to part a is:
$=356.43-37.58\approx\fbox{319 dollars per month}$
