Question

1. (38 points) A board of directors is considering installing double paned glass windows in its large office building. According to the accounting unit, the fixed costs (depreciation, maintenance, insurance) are annually 2000 euro more than for single paned glass windows. Natural gas costs 11 eurocents (100 cents 1 euro) per 10 megajoule (10'1), a year counts 2x10' seconds of heating and, on average, it is 10 °C warmer inside than outside. The heat transfer coefficients inside and outside are both 20 W/m2 °C. A glass window is 3 mm thick (Aelass 1 W/m C) and in between double paned glass (each side 3 mm thick glass) a) Calculate for single and double paned windows the annual energy loss (/m2 b) EXTRA (10 points) How large does the total surface of windows need to be for the company, such that the extra cost of double paned glass can be covered with the savings in heating costs?

Answer 1

Let inside temperature be 'T + 10' and outside temperature is 'T'

Overall heat loss is given by,

T+10-T loss,double 0.000.005 0.003

の106-48.514 (m2) = 48.544 2 Qloss.doubleー0.206

Now

Overall heat loss is given by,

-3333.33m2 2223 32 loss,single 0.003

0.106-48.544 (mi) = 48.544 2 Qloss.doubleー0.206

Let the surface area of window be 'A' m²

Let the fixed cost for sigle paned window be 'F'euro

Therefore fixed cost of double panned window be 'F+2000' euro

Total cost of window will be , T = Fixed cost + heating cost

For single paned

T = F + 3333.33 * A * 2 * 10⁷ * 0.11 * 10^-7............................................(1)

For doubled paned

T = F + 2000 + 48.544 * 2 * 10⁷ * A * 0.11 * 10^-7............................................(2)

Equating 1 and 2, we get

F+2000+ (48.544 × 2 x 10' × A × 0.11 x 10-')-F+ (3333.33 x 2 x 10' × A × 0. i î x 10-

$\Rightarrow 2000 = 361.326\times2\times A$

$\Rightarrow A = 2.77\left ( m^{2} \right )$

So area of window should be 5.5352 * 10^7 (m²)