1. EGR 334 Thermodynamics Chapter 3: Section 9-10
Lecture 08:
Specific Heat Capacity
Quiz Today?

2. Today’s main concepts:
Introduce Specific Heats, cv and cP.
Understand when it is acceptable to apply specific heat.
Calculate changes of energy using specific heats
For liquids and solids, the saturated properties values may be used to approximate properties values for supercooled property values, if the model can be treated as incompressible.
For incompressible liquids and solids, cv ≈ cp
the specific heat ratio is defined as k = cp/cv
Reading Assignment:
Read Chap 3: Sections 11
Homework Assignment:
From Chap 3: 49, 55,68, 78

3. Think back to those simple, happy, carefree days of your youth, back when you were in Physics lab….
You performed experiments to try and figure out how the world around you worked.
In one experiment you dropped hot aluminum pellets into a container of water and measured the change of temperature the water underwent.
… it requires 1 calorie
of heat to raise the
temperature of
1 gram of water
by 1 deg C.
Using that information you found a property of aluminum called
specific heat capacity.

4. -- Used to calculate changes of energy between states
Sec 3.9 : Specific Heat
In Thermodynamics, two common forms of specific heat capacity are used.
and
Constant Volume
process
Constant Pressure
process
-- Used to calculate changes of energy between states
-- Defined for pure, simple compressible substances
-- May be used only under certain “special conditions”
-- Usually applied to “ideal gas” model
When it can be applied: (if cv and cp are often treated as constants)
and

5. This is an exact differential
Sec 3.9 : Specific Heat
Specific Heats T v
isobars T1 T2
the internal energy change or enthalpy change when heat is added at constant pressure or constant volume.
At constant volume
This is an exact differential
where
At constant volume, dV=0; thus,
Finally:

6. This is an exact differential
Sec 3.9 : Specific Heat
isobars T v T1 T2
At Constant Pressure
This is an exact differential
where
At constant pressure, dP=0; thus,
Finally,

7. For air (at 68oF (20oC) and 14.7 psia (1 atm)):
Sec 3.9 : Specific Heat
Specific Heat Ratio:
For air (at 68oF (20oC) and 14.7 psia (1 atm)):

8. Fig03_09 Fig. 3.9 Shows that cv and cp for water/steam
vary with temperature and pressure.
Fig03_09

9. In practice, specific heats will be used as constants which are looked up on tables based on standard values of temperature and pressure.
Fig03_09
Example of Table:
Gases - Specific Heats and Individual Gas Constants

10. Evaluating Properties of Liquids and Solids:
While Appendix A does have a table for super-cooled water, for many other liquids, a super-cooled table is not available.
What to do?
For liquids and solids, it is acceptable practice to approximate
and
if a super cooled table is not available.

11. Evaluate liquids at the saturated state
Sec : Approximations for Liquids using Saturated Data
For a liquid, there is little change in v, u, h, s at different pressure and fixed T. Therefore,
Evaluate liquids at the saturated state
Since these properties are essentially only a function of T and not P, we call them Incompressible.

12. Example:
What is the enthalpy for Refrigerant 22 at T = 10 deg F. and p = 40 psi. (Refer to Table A-7E)
pressure
spec. vol. *
T=10 deg C
p = 40 psi
Temperature
spec. vol. * o
at T=10 deg….hf=13.33 Btu/lbm

13. For liquids and solids:
Sec : Incompressible Substance Model
Incompressible Substance: Includes any substance whose properties do not change with pressure.
For liquids and solids:
Thus
But,
So now what? Take partial with respect to T
Thus,

14. Use the heat capacity to calculate the change in internal energy.
Sec : Incompressible Substance Model
Use the heat capacity to calculate the change in internal energy.
If c = constant then that means,
is small and can usually be dropped
Therefore,

15. Table of specific heat for incompressible materials.
See the course website for the complete tables of specific heats for both compressible and incompressible materials.

16. End of Slides for Lecture 08