# Power Radiated From a Copper Cube

• Randomized10
Randomized10
Homework Statement
What power is radiated from a 340°C copper cube 1.0cm on a side? Assume an emissivity of 1

A. 0.76 W
B. 1.8 W
C. 3.4 W
D. 8.0 W
E. 19 W
Relevant Equations
$$\frac{dQ}{dt}=e\sigma AT^4$$
##e## is emissivity
##\sigma## is the Stefan-Boltzmann constant, ##5.67*10^{-8} W m^{-2} K^{-4}##
A is the surface area
T is the temperature
##\frac{dQ}{dt}## is the rate of heat transfer or radiated power

At first glance this appeared to be an easy problem, just plug in the values and go, so that's what I did. ##e=1##, ##\sigma=5.67*10^{-8} Wm^{-2}K^{-4}##, ##A=6*(1cm)^2=6*(0.01m)^2=6*0.0001m^2=0.0006m^2=6*10^{-4}m^2##, and ##T=340^{\circ}C=613.15K##. After plugging in the values I got ##\frac{dQ}{dt}=1*5.67*10^{-8}*6*10^{-4}*613.15^4=3.402*10^{-11}*1.4134*10^{11}=4.808W##, but that isn't one of the possible answers no matter how you round it. The answer key says that the correct answer is 19 W, but I don't know how to get there. I tried working out the math using Celsius instead of Kelvin, and got ##\frac{dQ}{dt}=0.4546W##, which isn't right either. Any insights as to what I'm doing wrong would be appreciated.

My calculation agrees with yours. This is not the first time that the correct solution does not match any of the offered answers. I suggest that you show your answer to the person who assigned you this problem because he/she/ze/they needs to know.

Randomized10
I agree with @kuruman. Your answer of 4.8 W looks correct. The answer of 19 W corresponds to an edge length of 2.0 cm.

Randomized10
Ok, I'll talk to the professor. Thank you!

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