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Heat capacity
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ID:(1618, 0)


Heat capacity
Description

Variables
Symbol
Text
Variable
Value
Units
Calculate
MKS Value
MKS Units
$C$
C
Caloric Capacity
J/K
$f$
f
Degrees of freedom
-
$n$
n
Número de Moles
mol
$m$
m
Particle mass
kg
$c_p$
c_p
Specific heat at constant pressure
J/kg K

Calculations

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Symbol
Equation
Solved
Translated

Calculations

Symbol
Equation
Solved
Translated

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Equations

Examples

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} n R_C $

(ID 3225)

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)

ID:(1618, 0)