What are some common mistakes students make with Stefan's Law?

Question

Sebastian Acosta · Accepted Answer

While considering Stefan's law, you must bear in mind :-

#1)# The body you consider must atleast approximate to a blackbody. Stefan's law holds only for black bodies.

#2)# If you are asked to experimentally verify Stefan's law using the torch bulb filament, be assured that you won't be able to obtain Stefan' law exactly from it. Power emitted will be proportional to #T^n# where #n# differs from #4#. So if you find out that #n# is #3.75#, you have done it right and you don't need to panic. (It is so primarily because a tungsten filament ain't a perfect blackbody).

#3)# Pay attention to the terms unit time and unit area. For a body with area A units, it has to be modified to #Q = sigma*A*T^4#. For a time #t#, multiply #Q# with #t#. However, most generally we deal with unit area and unit time. But, pay attention to the problem being asked.

#4)# As usual, pay attention to the units (whether they are all in the same system of units). Temperature is generally expressed in #K#.

#5)# The original Stefan's law states that power emitted by a perfect black body as radiation at temperature #T_1# per unit area, per unit time surrounded by another black body of temperature #T_2# is proportional to #(T_2)^4 - (T_1)^4#. But, when an external black body is absent, the expression reduces to #Q= sigma*T^4# where #T = T_1#.

William Audy · Answer

undefined Some common mistakes students make with Stefan's Law include:

1. Misunderstanding the formula: Students may incorrectly apply or interpret the formula $ P = \sigma A T^4 $, where $ P $ is the power emitted by a black body, $ \sigma $ is the Stefan-Boltzmann constant, $ A $ is the surface area of the object, and $ T $ is the temperature of the object in Kelvin.

2. Incorrect unit conversions: Since temperature must be in Kelvin for the formula to work correctly, students may forget to convert Celsius to Kelvin by adding 273.15.

3. Confusing the Stefan-Boltzmann constant: Students may use the wrong value for $ \sigma $ or forget to use it altogether, leading to incorrect calculations.

4. Neglecting surface area: Students may forget to consider the surface area of the object when applying Stefan's Law, especially when dealing with objects of irregular shape.

5. Forgetting to account for emissivity: Stefan's Law assumes that the object behaves like a perfect black body, emitting and absorbing all radiation. However, real objects have emissivity values less than 1, so students may forget to account for this factor in their calculations.

6. Ignoring other factors: Students may overlook other factors that can affect the emitted power, such as distance from the radiation source, surrounding temperature, and atmospheric conditions.