1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Specific heat and temperature

  1. Apr 12, 2007 #1
    Hi ,please I need something to begin this problem:

    The specific heat s of a material in [J/(kg deg C] is the amount of energy in joules required to raise the temperature of 1[kg] of material by one degree C. The density ρ of a material in [kg/m3] is the mass in [kg] per cubic meter. If a current density J exists inside a material for a time Δt, show that the rise in temperature Δ T in degree C given the formula (σ is conductivity of the material):

    Δ T=(J2* Δ t)/(s* σ* ρ)

    I don't know how to begin.
  2. jcsd
  3. Apr 12, 2007 #2
    Well I believe its pretty straight forward problem, assuming you know expression for Joule heating, normally expressed as I^2*R
    where I=current. Now consider the second part, the mass that is being heated and the constant that relates mass and heat to increase 1 degree. Is this any help?

    Incidentally as this may come up, the current density J is the same as I (total current) divided--or "normalized"--by the area thru which I flows thru. Conductivity (the reciprocal of resistance) is a normalized quantity. So the relation between J^2/conductivity is same as I^2*R
    Last edited: Apr 13, 2007
  4. Apr 13, 2007 #3
    I tried but I cannot make it right. I cannot the time and temperature in the expression.
    how can I introduce it?
    Last edited: Apr 13, 2007
  5. Apr 13, 2007 #4
    NP. Lets just look at the case of a resistor and we can fix it later if you don't get the normalization in last part of post I mentioned.

    I^2*R = rate of heat production (units of power). Multiplying by delta time gives total heat energy from Joule heating.

    Lets just say it was 6A and 5 Ohms of resistance;
    then heat production=180W Lets pick an arbitrary time of 10 seconds,
    then heat=1800 Watt seconds.(Joules)

    Lets say this was an aluminum block and assume no heat lost via transfer at surface so all energy goes into heating block.

    Heat capacity=0.9J/C-g where K is degrees Kelvin and g is one gram (see here if confused by term:


    Lets say block is 50 grams, the total temperature rise delta T (big T)
    Delta T=total heat energy/total heat capacity=1800/(50*0.9)

    Or 4.5 degrees. In this problem your constants are provided in consistent units, so no worries there.
  6. Apr 13, 2007 #5
    Ok I got it now
    Thank you!
  7. Apr 13, 2007 #6
    you're very welcome.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook