A circular window in the wall of a home has a diameter of 25 cm and is made of a single pane of glass 0.30 cm thick.Thermal conductivity for the glass is 0.63 W/mK.What heat is lost through the window in 12s if the temperature inside the house is 20$^{\circ}$C and outside is -12$^{\circ}$C?

Question

Quizplus · Accepted Answer

The rate of heat flow through a material is given by the equation:Q/t = kA(dT/dx)where:Q/t is the rate of heat flow in wattsk is the thermal conductivity of the material in W/mKA is the area of the material in m^2dT/dx is the temperature gradient in K/mIn this problem, we are given the following information:d = 25 cm = 0.25 mt = 0.30 cm = 0.0030 mk = 0.63 W/mKTi = 20oC = 293 KTo = -12oC = 261 KA = πd^2/4 = π(0.25 m)^2/4 = 0.0491 m^2We can use this information to calculate the rate of heat flow through the window:Q/t = kA(dT/dx)Q/t = (0.63 W/mK)(0.0491 m^2)(293 K - 261 K)/0.0030 mQ/t = 133.5 WThe heat lost through the window in 12 s is:Q = (133.5 W)(12 s) = 1602 J = 1.6 kJTherefore, the correct answer is A) 1.6 kJ.

A Circular Window in the Wall of a Home Has ∘^{\circ}∘

A Circular Window in the Wall of a Home Has $^{\circ}$