Isobar Heat capacity

Definition

The isobar heat capacity of a material, which one generally notes $C_p (T) ~$ , corresponds physically to the quantity of heat $d Q~$ which one must provide him to raise his temperature of a Kelvin, on the basis of $T~$ :

$d Q = C_p (T) \, D T$

Reciprocally, if the body in question cools of a Kelvin since the temperature $T~$ , it will release a quantity of heat also equalizes it with $d Q$ . In a more general way, to make pass the temperature of this body of $T_0~$ to $T_1~$ , the quantity of heat necessary is obtained by simple integration of the preceding relation:

$\ Delta Q = \ int_ {T_0} ^ {T_1} C_p (T) \, D T$

If the difference in temperatures between $T_0~$ and $T_1~$ is sufficiently weak so that the heat capacity does not vary, the quantity of preceding heat is expressed more simply:

$\ Delta Q = \ overline {C_p} \, (T_1 - T_0)$

with $\ overline {C_p}$ the median value of the heat capacity enters the two temperatures $T_0~$ and $T_1~$ .

In practice, this size is generally reported to the quantity of matter concerned and one speaks about heat capacity mass isobar or about heat capacity molar isobar according to the manner used to quantify the matter. The unit used is then the Joule by Kilogram and Kelvin (J·kg^-1·K^-1) or the Joule by Mole and Kelvin (J·mol^-1·K^-1).

Category: Thermodynamics

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