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Heat capacity
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ID:(1618, 0)


Heat capacity
Equation

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Caloric capacity is the heat or energy \ delta that is required to raise the temperature by dT , which is expressed as\\n\\n

$\delta Q = C_V dT$

\\n\\nIf the energy of n moles, with N_A the Avogadro number, k_B is the Boltzmann constant and T the temperature is\\n\\n

$U=\displaystyle\frac{f}{2}nN_Ak_BT$

\\n\\nso if the volume is kept constant\\n\\n

$dU=\delta Q=\displaystyle\frac{f}{2}nN_Ak_BdT$

\\n\\nso with\\n\\n

$R=k_BN_A$



you have

$C_V=\displaystyle\frac{f}{2}nR$

ID:(3225, 0)


Specific heat
Equation

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Specific heat corresponds to caloric capacity per mass

$c_V=\displaystyle\frac{C_V}{M}$



If m is the mass of an atom, the mass M will be

$M=nN_Am$



with n the number of moles and N_A the number of Avogadro. As the caloric capacity is

$C_V=\displaystyle\frac{f}{2}nkN_A$



so the specific heat is

$ c_V =\displaystyle\frac{ f k_B }{2 m }$

ID:(3941, 0)