Stefan-Boltzmann Lab: Exploring Exponent of R vs T

In summary, the experiment involved empirically determining the exponent on the Stefan-Boltzmann law using a light bulb and measuring the voltage and current across it. The equation P=k*(R/c)^n was used and the logarithm of both sides was taken to give ln P=const + nlnR. The slope of the graph of ln P vs. ln R was measured to be 2.78, which is different from the expected value of 4. However, the line was nearly perfect and many others who did the experiment also got similar results. The question is why the value of 2.78, and it is suggested that the resistivity of the tungsten wire in the bulb may have a power 2 relationship
  • #1
ideasrule
Homework Helper
2,286
0

Homework Statement


A few weeks ago I did an experiment that involved empirically determining the exponent on the Stefan-Boltzmann law. I used a light bulb and measured the voltage and current across it for different voltages. Since P=k*Tn and R=cT (i.e. resistance of the filament is proportional to temperature), P=k*(R/c)n. Taking the logarithm of both sides gives ln P=const + nlnR. At equilibrium, the bulb should emit just as much power in the form of blackbody radiation as the power supply provides, so P=VI.

I graphed ln P vs. ln R and measured the slope of the line: 2.78, a far cry from 4. However, the line was nearly perfect! All of the points were nearly touching the line of best fit I drew! Moreover, many other people did this experiment, and almost all of them got 2.5-2.9.

My question is: why 2.78?

The Attempt at a Solution



I'm thinking that if R doesn't increase linearly with T but is instead proportional to a power of T, the value of 2.78 would make sense. However, that's clearly an ad hoc approach. I've no idea why R would be proportional to anything other than T.

Edit: Please reply quickly, because I'm kind of on a deadline.
 
Last edited:
Physics news on Phys.org
  • #2
ideasrule said:


My question is: why 2.78?

The Attempt at a Solution



I'm thinking that if R doesn't increase linearly with T but is instead proportional to a power of T, the value of 2.78 would make sense. However, that's clearly an ad hoc approach. I've no idea why R would be proportional to anything other than T.

Edit: Please reply quickly, because I'm kind of on a deadline.


You are right, the temperature dependence of the resistivity of the tungsten wire in the bulb is rather a power 2 relationship at high temperatures than linear.

http://hypertextbook.com/facts/2004/DeannaStewart.shtml

ehild
 
  • #3


I would first like to commend you on your thorough and well-executed experiment. It is clear that you put a lot of thought and effort into your measurements and analysis.

The value of 2.78 for the exponent on the Stefan-Boltzmann law is indeed interesting. It is not uncommon for experimental results to deviate from the expected value, especially when dealing with complex physical phenomena. It is possible that there are other factors at play that may affect the relationship between power and resistance, such as the shape and material of the light bulb filament.

One possible explanation for the value of 2.78 is that it represents an average of all the individual factors that contribute to the overall resistance-temperature relationship. It is possible that some factors may have a stronger influence than others, resulting in a slightly lower exponent. Additionally, the precision of your measurements and experimental setup may also contribute to the observed value.

To further investigate this, I would suggest conducting additional experiments with different types of light bulbs, varying the voltage and current, and using different materials for the filament. This may help to identify any potential factors that could explain the deviation from the expected value of 4.

Overall, your experiment has provided valuable insights into the Stefan-Boltzmann law and has sparked further curiosity and questions. I encourage you to continue exploring this topic and to share your findings with others in the scientific community.
 

1. What is the Stefan-Boltzmann Law?

The Stefan-Boltzmann Law is a physical law that describes the relationship between the temperature of an object and the amount of thermal radiation it emits. It states that the total energy radiated per unit surface area of a black body is proportional to the fourth power of its absolute temperature.

2. What is the purpose of the Stefan-Boltzmann Lab?

The purpose of the Stefan-Boltzmann Lab is to explore the relationship between the exponent of the Stefan-Boltzmann Law and the temperature of an object. This lab allows for a hands-on understanding of the principles behind the law and its applications in the field of thermodynamics.

3. How is the exponent of the Stefan-Boltzmann Law related to temperature?

The exponent of the Stefan-Boltzmann Law, also known as the "Stefan-Boltzmann constant," is directly related to temperature. As temperature increases, the amount of thermal radiation emitted by an object also increases, resulting in a higher exponent value. This relationship is described by the equation e = σT^4, where e is the exponent and T is the temperature in Kelvin.

4. Can the Stefan-Boltzmann Law be applied to all objects?

The Stefan-Boltzmann Law can be applied to all objects that emit thermal radiation, but it is most accurate for objects that behave like ideal black bodies. This means they absorb and emit all wavelengths of radiation equally and have a perfectly efficient energy transfer.

5. How is the Stefan-Boltzmann Law used in real-world applications?

The Stefan-Boltzmann Law has many real-world applications, including measuring the energy output of stars, determining the energy efficiency of buildings, and calculating the temperature of planets and other celestial bodies. It is also used in engineering and manufacturing processes to control and measure thermal radiation in various systems.

Similar threads

  • Introductory Physics Homework Help
Replies
5
Views
3K
  • Advanced Physics Homework Help
Replies
4
Views
4K
  • Introductory Physics Homework Help
Replies
4
Views
3K
Replies
1
Views
526
  • Other Physics Topics
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
4K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Advanced Physics Homework Help
Replies
1
Views
2K
Replies
2
Views
24K
Back
Top