Specific Heat

Energy Analysis of Closed Systems

To reiterate…
Intensively
$h+u+Pv$ Where there is also an extensive form.

Two Types of Specific Heat

Constant Volume

$du=c_{v}dT$ $u_2-u_2=\overline{c_v}\left(T_2-T_1\right)$

Constant Pressure

$dh=c_{p}dT$
$h_2-h_1=\overline{c_p}\left(T_2-T_1\right)$
$q_v=q_p$ which means $\Delta u<\Delta h$ and $c_v<c_p$

For an Ideal Gas

$h=u+P_v=u+RT$
At Constant Pressure $c_p=\frac{dh}{dT}=\frac{du}{dt}+R=c_v+R$

Finding c_p or c_v

If you know $c_p$ or $c_v$ you can find the other one

For a Solid or a Liquid

At Constant Pressure $h=u+Pv$ $dh=du+Pdv$ If incompressible then Pdv = 0 and… $c_p=c_v=c$

Specific Heat Ration

Often you’re given a specific heat ratio
$k=\frac{c_p}{c_v}$