2/2     Dear motd physicists, suppose I have a) 5 100W light bulbs and b) 500W
        heater. Suppose put them in 2 different thermal tight boxes, each with
        a liter of water. Will both liter of water have the exact same
        temperature after time t?
        \_ No, because 5 light bulbs have a different heat capacity than a
           500W heater.  If they were the same, then yes, the water would have
           the same temperature.  There are of course special cases where this
           would be different, but 5x100W light bulbs create just as much heat
           as a 500W heater.
           \_ You just contradicted yourself.
              \_ He didn't really. He said they create just as much heat, but
                 have different heat capacities. Although I'm curious about the
                 special cases she mentions.
                 \_ I was thinking stuff like differential evaporation rates
                    and transient higher electrical loads.
        \_ One thing to note is that by saying a light bulb is X wats, it does
           not mean that it puts out X watts of heat; it just means it draws
           X watts of energy. What is does with those X watts depends on
           the type of bulb and other details like that.
           \_ It can basically only put off various forms of electromagnetic
              energy and sound.  If it's placed in a perfect calorimeter
              (OP's 'thermal tight box') then all the energy it consumes will
              be turned into heat.
        \_ You're probably limited by the conductive heat transfer at the
           air-water interface.  Probably the only difference between the two
           rigs is how much energy goes into visible vs. infrared, and that
           probably won't matter as the water won't likely heat up very much.
           \-to spell out the first reply:
             the simple way to thinks of this is in terms of the Partition Of
             Energy. the energy in the system will be divided between the
             water and the heating apparatus. at T0, with energy E0 = Ew0 +
             Eh0 (or Eb0) [total energy = energy of water + energy of bulb/
             heater]. at T1, E1 = E0+dE = Ew1 + Eh1 (Eb1). Since we are
             assuming dE is the same in both, Ew1 is identical iff the Eh1
             and Eb1 are the same ... which is dictated by the heat capacity.
             [and the heat capacity of the water is how you go from the
             Ew to the water temp]. Note: in some cases the parition of
             energy is more complicated and you have to taken into
             consideration entropy factors. Like say you mix metal A and B
             into an alloy ... as the compositoon goes from 100% A to 100% B,
             the melting temp of AB doesnt go in a stright line from meltA
             to meltB.
             \- oh here is another one: you take a spring and spend energy E
                to compress it. then you put it in an acid bath, where does
                the energy go, if it dissolves from the end.
                \_ In a compressed spring, the energy is stored in the bonds
                   between atoms.  As it dissolves, these bonds get broken one
                   by one, and when that happens, the 2 atoms whoose bond was
                   dissolved convert that bond energy into heat.  So a
                   dissolved compressed spring will be hotter than a dissolved
                   relaxed spring.