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Thermodynamics problem

  1. Sep 22, 2016 #1
    1. The problem statement, all variables and given/known data

    A silicon electric circuit is 23 mg, when electricity flows through the circuit rising the energy by 7.4 mW but this circuit wasn't design for heat ventilation. Find the rate of how much the temperature is rising per second ( ΔT/Δt ) The specific heat of silicon is 705 J/kg.K


    2. Relevant equations
    Q=mcΔT

    3. The attempt at a solution

    I know that when the electricity flows through the circuit, it will rise the temperature and we can figure the change in temperature by find both initial and final temperature but what about time? how this factor get in the calculation?
     
    Last edited: Sep 22, 2016
  2. jcsd
  3. Sep 22, 2016 #2

    DrClaude

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    Can you express watts in terms of other SI units?
     
  4. Sep 22, 2016 #3

    Bystander

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    Ask not for whom the bell tolls. Ask instead "the bell's heat capacity."
     
  5. Sep 22, 2016 #4
    Joules per second ? it is just a rate of how much energy was transfer in 1 second, I can't plug this in Q :/
     
  6. Sep 22, 2016 #5

    DrClaude

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    No, but you can calculate Q/Δt :smile:
     
  7. Sep 22, 2016 #6
    hmm I don't know if I am correct or not

    from Q=mcΔT and ΔT/Δt
    (Q/mc) / Δt = Q / (mc)Δt
    7.4x10-3 J / (23x10-6kg)x(705 J/kg.K)x 1 s
    = 0.46 K/s
     
    Last edited: Sep 22, 2016
  8. Sep 22, 2016 #7

    DrClaude

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    Be careful with the mass there. Since you are given the heat capacity per gram, you can use g throughout and not convert to kg.

    Also, I would find it more appropriate to take Q/Δt as a whole to be 7.4 mW instead of "assuming" 1 second.
     
  9. Sep 22, 2016 #8
    edited
    Then Q / (mc)Δt = W/mc
    (7.4x10-3 W ) / (23x10-6kg)(705 J/kg.K)
    = 0.46 K/s

    but how this equation solve the problem?
     
    Last edited: Sep 22, 2016
  10. Sep 22, 2016 #9

    DrClaude

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    You've missed a division in there.
     
  11. Sep 22, 2016 #10
    oops, sorry. I've edited them and got the same answer 0.45-0.46 K/s
    I think this is another pure mathematic problem :( really hate this kind of problem.
     
  12. Sep 22, 2016 #11

    DrClaude

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    I wouldn't say that this is "pure mathematics." Actually, you need physical insight to figure out that you have information about Q/Δt. Once you figure that out, you have
    $$
    \frac{Q}{\Delta t} = m c \frac{\Delta T}{\Delta t}
    $$
    and you simply need to rearrange the equation to isolate ##{\Delta T}/{\Delta t}##, which is what you are asked for. Such simple algebra appears everywhere in physics, so you better get used to it (and good at it) :smile:
     
  13. Sep 22, 2016 #12
    Never see that equation before :/

    I don't know how come Q=mcΔT so I don't actually understand how to use it
     
  14. Sep 22, 2016 #13

    DrClaude

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