An electric kitchen range has a total wall area of 1.40 m^2 and i...

Question

An electric kitchen range has a total wall area of 1.40 m^2 and is insulated with a layer of fiberglass 4.00 cm thick. The inside surface of the fiberglass has a temperature of 175°C, and its outside surface is at 35.0°C. The fiberglass has a thermal conductivity of 0.040 W/m K. (a) What is the heat current through the insulation, assuming it may be treated as a flat slab with an area of 1.40 m^2 ?

Accepted Answer

Welcome back everybody. We are told that an oven is fitted with some sort of insulated surface and we're told a couple things about this insulated service. First off that it's made of rock wall and has, sorry, let me change color here real quick. Has an area of 0.12 m squared. We are also told that it is two centimeters thick or 20.2 m thick. We are told that the rock wool has a thermal conductivity of 0.4 watts per meter kelvin. And at one particular instance on the inside of the insulated surface, it heats up to 100 and 50 degrees Celsius and then on the outside it just remains room temperature which is 25 degrees Celsius. And we are tasked with finding what the heat current flowing through the rock is. So heat with respect of time, we need to figure out what that is. Well, We have a formula for this. Our formula states that are heat current is equal to our thermal conductivity constant times the area of the surface, times the change in temperature or the difference in temperature all over the thickness of the insulated material. We have all of that. So let's just go ahead and plug in our values, our heat current is equal to 0. times are area of 0.12 times the difference in temperature. Now we are supposed to work, be working in kelvin and we're working in Celsius here. But even if we convert to kelvin, the difference between the two values is still going to be the same. So the difference is still 100 In 25°C or 125° Alvin. And this is all over the thickness of .02 m, which when you plug into your calculator, we get that the heat current flowing through is 30 watts corresponding to our answer choice of C. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.

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