Heat capacity: Difference between revisions

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The '''heat capacity''' is given by the differential of the heat with respect to the [[temperature]],
The '''heat capacity''' is given by the differential of the heat with respect to the [[temperature]],


:<math>C = \frac{\delta Q}{\partial T}</math>
:<math>C := \frac{\delta Q}{\partial T}</math>
==At constant volume==
==At constant volume==
At constant volume (denoted by the subscript <math>V</math>),
At constant volume (denoted by the subscript <math>V</math>),
:<math>C_V = \left.\frac{\delta Q}{\partial T} \right\vert_V = \left. \frac{\partial U}{\partial T} \right\vert_V </math>
:<math>C_V := \left.\frac{\delta Q}{\partial T} \right\vert_V = \left. \frac{\partial U}{\partial T} \right\vert_V </math>




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==At constant pressure==
==At constant pressure==
At constant pressure (denoted by the subscript <math>p</math>),
At constant pressure (denoted by the subscript <math>p</math>),
:<math>C_p = \left.\frac{\delta Q}{\partial T} \right\vert_p = \left. \frac{\partial U}{\partial T} \right\vert_p + p \left.\frac{\partial V}{\partial T} \right\vert_p</math>
:<math>C_p := \left.\frac{\delta Q}{\partial T} \right\vert_p = \left. \frac{\partial U}{\partial T} \right\vert_p + p \left.\frac{\partial V}{\partial T} \right\vert_p</math>





Revision as of 16:44, 8 July 2008

From the first law of thermodynamics one has

where is the heat, is the internal energy, is the pressure and is the volume. The heat capacity is given by the differential of the heat with respect to the temperature,

At constant volume

At constant volume (denoted by the subscript ),


At constant pressure

At constant pressure (denoted by the subscript ),


The difference between the heat capacity at constant pressure and the heat capacity at constant volume is given by