How much heat is lost in an hour through a glass window measuring

Question

How much heat is lost in an hour through a glass window measuring 2.0 m by 2.5 m when inside temperature is 25 °C and that of outside is 5°C, the thickness of glass is 0.8 cm and the value of k for glass is 0.8 W m – 1 K-1 ? $(3.6 imes10 7 J)$

Accepted Answer

Solution: Time = t = 1hour = 3600 s

Thickness of glass = L = 0.8 cm =$\frac{0.8}{100 }$= 0.008 m

Area of a glass window = A = $2.0 m imes 2.5$ m = $5 m^{2}$

Temperature outside the house = $T_{1}$ = 25°C = 25 + 273 = 298 K

Temperature inside the house = $T_{2}$ = 5°C = 5 + 273 = 278 K

Change in temperature = $ riangle T$ = $T_{1} - T_{2}$ = 298 – 278 = 20 K

Value of conductivity for concrete = k = $0.8 W m^{-1} K^{-1}$

Rate of conduction of thermal energy =$\frac{Q}{t}$=?

$\frac{Q}{t}$ = $\frac{(〖kA(T〗_{1} – T_{2}))}{L}$

Q =$\frac{(〖kA(T〗_{1} – T_{2}))}{L} imes t$

$\frac{Q}{t}$= $\frac{(0.8 imes 5 imes 20)}{0.008 imes3600}$= $80/0.008 imes 3600$= 36,000,000 J = $3.6 imes 10$ 7 J