5 ms·

Sure it can - you just have to focus the sun's rays into a smaller area. The sun delivers on the order of 1000W per sqm during the day, so (eg.) focusing 100 s

Sure it can - you just have to focus the sun's rays into a smaller area. The sun delivers on the order of 1000W per sqm during the day, so (eg.) focusing 100 sqm into 1 sqm == 100,000W. 12 hours of daylight will then give you a theoretical production of 1.2MWh per day, but it's usually a lot less, due to the angle of the sun in the morning/evening and inefficiencies in your energy capture.

kjuhygtfrde 16y ago
On HN we obey the 2nd law of thermodynamics
- anthonyb 16y ago
  That entropy always increases? How exactly does that apply in the case of focusing photons?
  - kjuhygtfrde 16y ago
    Another way of stating it is that heat flows from hot->cold. You can't concentrate the light/heat from a blackbody source to more than the temperature of the source. So you can't focus sunlight to more than 6000k however many mirrors you use.
    - btilly 16y ago
      The laws of thermodynamics do not prevent energy from flowing from cold to hot. They just say that for that to happen, entropy elsewhere must increase more. As a trivial example disproving your claim, energy from the Sun can be collected in solar panels that can be used to run devices that can hit any temperature you want. For an extreme example, for fusion experiments they produce temperatures of over 11,000,000 degrees C. For another trivial example, most of us have refrigerators that can transport heat energy from a colder place (the inside of the fridge) to a warmer place (your kitchen).
  - ramchip 16y ago
    Disclaimer: not a physicist. My intuitive understanding is that, as you heat the absorber, it becomes hotter and hotter, until it reaches the same temperature as the sun's surface. At this point, the absorber (also a blackbody) radiates just as much energy as it receives from the sun; thus there is no more heat exchange. Otherwise, you would be taking two objects at the same temperature and making one hotter and the other one colder with no work from outside the system, violating thermodynamics. There is a more formal study in solar energy books like (http://books.google.com/books?id=81WI2LwrpkcC&lpg=PA25&ots=PZpR4ybY16&dq=limit%20temperature%20blackbody&pg=PA25#v=onepage&q&f=false http://books.google.com/books?id=81WI2LwrpkcC&lpg=PA25&#...) or (http://www.physics.drexel.edu/~jenks/Solar%20Energy.pdf http://www.physics.drexel.edu/~jenks/Solar%20Energy.pdf) (PDF, page 21 onwards is quite relevant).
    - anthonyb 16y ago
      Your intuition seems wrong to me. The two major problems are that thermodynamics refers to energy, not temperature. Thus, as long as total energy is conserved, there's no problem. The second issue is that solar heating is due to radiation, not conduction/convection, so there's no heat exchange as such. Think of it in terms of photons - if you're collecting and concentrating photons, the upper limit is the total number of photons which the sun produces. I'm pretty sure that if you focused all of those into a square meter of the earth's surface, then it'd reach more than 5760K.
      - gbhn 16y ago
        You can't do that (at least not with passive components). There's a famous optics result called the 'brightness theorem' that explains why not.
        anthonyb 16y ago
        I think you mean "Conservation of radiance". It corresponds pretty much directly with "Power per unit area". Obviously, mirrors and lenses can reduce the unit area, while keeping power constant (at best). http://en.wikipedia.org/wiki/Radiance#Intensity http://en.wikipedia.org/wiki/Radiance#Intensity

kjuhygtfrde 16y ago

On HN we obey the 2nd law of thermodynamics

anthonyb 16y ago
That entropy always increases? How exactly does that apply in the case of focusing photons?
- kjuhygtfrde 16y ago
  Another way of stating it is that heat flows from hot->cold. You can't concentrate the light/heat from a blackbody source to more than the temperature of the source. So you can't focus sunlight to more than 6000k however many mirrors you use.
  - btilly 16y ago
    The laws of thermodynamics do not prevent energy from flowing from cold to hot. They just say that for that to happen, entropy elsewhere must increase more. As a trivial example disproving your claim, energy from the Sun can be collected in solar panels that can be used to run devices that can hit any temperature you want. For an extreme example, for fusion experiments they produce temperatures of over 11,000,000 degrees C. For another trivial example, most of us have refrigerators that can transport heat energy from a colder place (the inside of the fridge) to a warmer place (your kitchen).
- ramchip 16y ago
  Disclaimer: not a physicist. My intuitive understanding is that, as you heat the absorber, it becomes hotter and hotter, until it reaches the same temperature as the sun's surface. At this point, the absorber (also a blackbody) radiates just as much energy as it receives from the sun; thus there is no more heat exchange. Otherwise, you would be taking two objects at the same temperature and making one hotter and the other one colder with no work from outside the system, violating thermodynamics. There is a more formal study in solar energy books like (http://books.google.com/books?id=81WI2LwrpkcC&lpg=PA25&ots=PZpR4ybY16&dq=limit%20temperature%20blackbody&pg=PA25#v=onepage&q&f=false http://books.google.com/books?id=81WI2LwrpkcC&lpg=PA25&#...) or (http://www.physics.drexel.edu/~jenks/Solar%20Energy.pdf http://www.physics.drexel.edu/~jenks/Solar%20Energy.pdf) (PDF, page 21 onwards is quite relevant).
  - anthonyb 16y ago
    Your intuition seems wrong to me. The two major problems are that thermodynamics refers to energy, not temperature. Thus, as long as total energy is conserved, there's no problem. The second issue is that solar heating is due to radiation, not conduction/convection, so there's no heat exchange as such. Think of it in terms of photons - if you're collecting and concentrating photons, the upper limit is the total number of photons which the sun produces. I'm pretty sure that if you focused all of those into a square meter of the earth's surface, then it'd reach more than 5760K.
    - gbhn 16y ago
      You can't do that (at least not with passive components). There's a famous optics result called the 'brightness theorem' that explains why not.
      - anthonyb 16y ago
        I think you mean "Conservation of radiance". It corresponds pretty much directly with "Power per unit area". Obviously, mirrors and lenses can reduce the unit area, while keeping power constant (at best). http://en.wikipedia.org/wiki/Radiance#Intensity http://en.wikipedia.org/wiki/Radiance#Intensity