A cube of copper of mass 8 kg and initial temperature of 110 oC is set to radiat

Question

A cube of copper of mass 8 kg and initial temperature of 110 oC is set to radiatively cool in an environment of 100 oC. (Note: copper has an emissivity of about 0.05. Also, neglect conduction and convection as cooling agents in this problem.) a.) What is the total outside surface area of this cube?____m2 b.) Before the copper has had a chance to cool, find the net rate of heat transfer of the cube to the environment. Initially, Pcube =exactly:____W....in the Newton's cooling approximation:____W....size of % error in approximation=____% (Answer + only.) c.) Using the approximation, find: the time constant (?) for this system: ____min....the time it takes for the cube to cool within 1oC of the environment:____min d.) Revisiting part b, re-estimate the validity of the approximation for this 1oC temperature difference: Now, Pcube =exactly:____W....in the Newton's cooling approximation:____W....size of % error =____% (Answer + only.)

Explanation / Answer

Using Pnet=Aes(to^4-ts^4), s=stefan boltzman constant, to= temp of object, ts= temp of surroundings, e=emissivity, a= surface area (.035)(.05)(5.67*10^-8)(383.15^4-373.15^4)=.215 W

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