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How much heat required to raise the temperature of potassium

  1. Jun 7, 2016 #1
    1. The problem statement, all variables and given/known data
    At low temperatures, the specific heats of metals is described by the expression
    ## c=kT + AT^3 ##
    , where k and A are constants. Here the first term describes the contribution of free electrons and the second the lattice contribution.
    How much heat is required to raise the temperature of 1 g of potassium from 1 K to 5 K?
    For potassium, ## k=\frac{2.1mJ}{(mol K^2)} \\ \\ \\ A=\frac{2.6mJ}{(mol K^4)} ##

    2. Relevant equations
    Above
    ##M##gram ##=\frac{1}{\mu}##mol
    3. The attempt at a solution
    ## C= \frac{\Delta Q}{\Delta T M} ##
    Wheareas: ##\Delta Q## is the change in the amount of heat , ##\Delta T## is the change in the temperature.
    ## \Delta Q = CM \Delta T = (kT+AT^3)M\Delta T ##
    ## \int dQ = \frac{1}{\mu} \int ^{T_2} _{T_1} (kT+AT^3)dT ##
    ## Q = \frac{1}{\mu} (\frac{KT^2}{2} + \frac{AT^4}{4})^{T_2} _{T_1} ##
    ##T_1 = 1## ##T_2 = 5## (is this correct?)
    Did I use the formula correctly , if so , could you help me with the the integration factors please.
    Thanks in advance.
     
  2. jcsd
  3. Jun 7, 2016 #2
    Yes, it's correct.
     
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