FL: Heat Capacities and Latent Heat

"Heat Capacity"

Consider two closed systems to which you add heat ...

$\Delta u + \Delta e_{k} + \Delta e_{p} = w + q $

cp/cv schematic

$\Delta e_{k} = \Delta e_{p} = w = 0 $

$\Delta u = q $

$\Delta e_{k} = \Delta e_{p} = 0 $

$\Delta u = q + w = q - P\Delta v$

$\Delta h = \Delta u + P\Delta v = q $

For convenience the "other" intensive property is chosen to be temperature ... why?


The heat capacity at constant volume is defined as:

$c_v \equiv \left ( \frac{\partial u}{\partial T} \right )_v$


The heat capacity at constant pressure is defined as:

$c_P \equiv \left ( \frac{\partial h}{\partial T} \right )_P$


For solids and liquids: $c_v \approx c_P$ why?

For ideal gases: $c_P = c_v + R$ why?

For real gases: $c_P > c_v$


Heat capacities are state functions (depend on T!).

Test Yourself:

Verify if the "cold water diet" would work. Some joker proposed that drinking 0.5kg of ice-cold water at each meal would be an effective diet method. Determine the internal energy change this would cause. What if you used ice cubes instead of water?


The latent heat is the specific enthalpy change associated with a change in state of aggregation (phase).


The latent heat is often known only at a single temperature, yet this state function is, of course, dependent on temperature. How do we handle that?.