- #1
Alettix
- 177
- 11
Hello!
This is an old problem from the Estonian-Finnish open physics olympiad (2013) and I hope you will be able to lend me some help.
1. Homework Statement
Sun-rays are focused with a lens of diameter d = 10 cm and focal length f = 7 cm to a black thin plate. Behind the plate is a mirror. Angular diameter of the sun is α = 32' and its intensity on the surface of Earth is I = 1000 W/m2
i) Find the temperature of the heated point of the plate.
ii) Using thermodynamic arguments, estimate the maximal diameter of the lens for which this model can be used.
The lens formula: ## \frac{1}{a} + \frac{1}{b} = \frac{1}{f} ##
Magnification: ## \frac{a}{b} = \frac{y'}{y} ##
Stefan-Boltzmann law: ## \frac{P}{A} = \sigma T^4 ##
i) Is not a problem, however I got really stuck on ii), so I checked the solution and could read the following: " Due to the second law of thermodynamics, it is impossible to direct heat energy from a lower temperature body to a higher temperature body. Hence, the image temperature cannot exceed the temperature of the Sun.". This statement was followed by easy calculations, but I have not really been able to accept this statement completely and would appreciate if you could help me out.
When two bodies are placed in contact, it is intuitive that the hotter one will not get hotter while the colder cools down. It is also understandable with a microscopic perspective, because the molecules will transport energy from the hotter body to the cooler by collisions, and not the other way around. However, I have never previously encountered the second law of thermodynamics being applied to radiation. Here, the microscopic picture consists of photons with different energies hitting a plate. Assuming that the plate absorbs all radiation, I can't see why more incoming photons couldn't heat the material even more (for instance if we increase the diameter of the lens). I mean, there is no property other than the spectral distribution of the photons showing what temperature the body they are radiated from have. However, if we look at the photons one by one nothing can tell us how hot that body is, and consequently they should be able to give of their energy to the plate and heat it above the temperature of the sun. Where am I thinking wrong?
Thank you in advance! :)
This is an old problem from the Estonian-Finnish open physics olympiad (2013) and I hope you will be able to lend me some help.
1. Homework Statement
Sun-rays are focused with a lens of diameter d = 10 cm and focal length f = 7 cm to a black thin plate. Behind the plate is a mirror. Angular diameter of the sun is α = 32' and its intensity on the surface of Earth is I = 1000 W/m2
i) Find the temperature of the heated point of the plate.
ii) Using thermodynamic arguments, estimate the maximal diameter of the lens for which this model can be used.
Homework Equations
The lens formula: ## \frac{1}{a} + \frac{1}{b} = \frac{1}{f} ##
Magnification: ## \frac{a}{b} = \frac{y'}{y} ##
Stefan-Boltzmann law: ## \frac{P}{A} = \sigma T^4 ##
The Attempt at a Solution
i) Is not a problem, however I got really stuck on ii), so I checked the solution and could read the following: " Due to the second law of thermodynamics, it is impossible to direct heat energy from a lower temperature body to a higher temperature body. Hence, the image temperature cannot exceed the temperature of the Sun.". This statement was followed by easy calculations, but I have not really been able to accept this statement completely and would appreciate if you could help me out.
When two bodies are placed in contact, it is intuitive that the hotter one will not get hotter while the colder cools down. It is also understandable with a microscopic perspective, because the molecules will transport energy from the hotter body to the cooler by collisions, and not the other way around. However, I have never previously encountered the second law of thermodynamics being applied to radiation. Here, the microscopic picture consists of photons with different energies hitting a plate. Assuming that the plate absorbs all radiation, I can't see why more incoming photons couldn't heat the material even more (for instance if we increase the diameter of the lens). I mean, there is no property other than the spectral distribution of the photons showing what temperature the body they are radiated from have. However, if we look at the photons one by one nothing can tell us how hot that body is, and consequently they should be able to give of their energy to the plate and heat it above the temperature of the sun. Where am I thinking wrong?
Thank you in advance! :)