Some properties of a certain glass are listed here: Density 2300 kg/m³
Specific heat capacity 840 J/kg ? C°
Coefficient of thermal expansion 8.5 × 10^-6 (C°) ^-1
Thermal conductivity 0.80 W/m ? C°
A glass window pane is 2.7 m high, 2.4 m wide, and 9.0 mm thick. The temperature at the inner surface of the glass is $19 ^ { \circ } \mathrm { C }$ and at the outer surface 4°C. How much heat is lost each hour through the window?

Question

Some properties of a certain glass are listed here: Density 2300 kg/m³
Specific heat capacity 840 J/kg ? C°
Coefficient of thermal expansion 8.5 × 10^-6 (C°) ^-1
Thermal conductivity 0.80 W/m ? C°
A glass window pane is 2.7 m high, 2.4 m wide, and 9.0 mm thick. The temperature at the inner surface of the glass is

19 ^ { \circ } \mathrm { C }

and at the outer surface 4°C. How much heat is lost each hour through the window?

Quizplus · Accepted Answer

The rate of heat flow through a material is given by the equation:$$Q = kA\frac{dT}{dx}$$where:* Q is the rate of heat flow (in watts)* k is the thermal conductivity of the material (in W/m-K)* A is the area of the material (in m^2)* dT/dx is the temperature gradient across the material (in K/m)In this problem, we are given the following information:* k = 0.80 W/m-K* A = 2.7 m * 2.4 m = 6.48 m^2* dT = 19°C - 4°C = 15°C* dx = 9.0 mm = 0.009 mPlugging these values into the equation, we get:$$Q = (0.80 W/m-K)(6.48 m^2)(15°C/0.009 m) = 7.2 × 10^3 W$$Since we want to know the amount of heat lost each hour, we need to multiply this value by the number of hours in an hour:$$Q = (7.2 × 10^3 W)(1 hr) = 3.1 × 10^7 J$$Therefore, the correct answer is A.

Some Properties of a Certain Glass Are Listed Here: Density 19∘C19 ^ { \circ } \mathrm { C }19∘C

Some Properties of a Certain Glass Are Listed Here: Density $19 ^ { \circ } \mathrm { C }$