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FIRST LAW OF THERMODYNAMICS. CONSERVATIVE APPLICATION OR REDUCTION OF ENERGY TO AN ATMOSPHERIC SYSTEM
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1. SO345: Atmospheric Thermodynamics CHAPTER 6: THE FIRST LAW
OF THERMODYNAMICS
5. FIRST LAW OF THERMODYNAMICS
CONSERVATIVE APPLICATION OR REDUCTION OF ENERGY TO AN ATMOSPHERIC SYSTEM
6. FIRST LAW OF THERMODYNAMICS
net flow of energy across system boundaries is equal to the net change in energy of the system.
7. FIRST LAW OF THERMODYNAMICS .
ENERGY CAN NEITHER BE CREATED NOR DESTROYED; ONLY TRANSFERED OR TRANSFORMED!
8. FIRST LAW OF THERMODYNAMICS
Energy is the capacity of a system to do work.
The dimensions of energy are the same as for work and heat:
[ M L2 T-2]
with units of Joules and ergs.
9. FIRST LAW OF THERMODYNAMICS INTERNAL ENERGY
If we allow a system to go from an initial equilibrium state (defined at some p, T, ?) to a final equilibrium state (defined at another p, T, ?) by adding heat (?H) to the system, and having work done (?W) by the system, the difference in internal energy (?U) will be defined by:
?U = ?H - ?W.
10. FIRST LAW OF THERMODYNAMICS INTERNAL ENERGY
And in differential form, where the system undergoes an infinitesimal change in state:
dU = dH - dW (Eq 6.1)
where:
dH = infinitesimal amount of heat added to the system
dW = infinitesimal amount of work done
dU = infinitesimal internal energy change
11. FIRST LAW OF THERMODYNAMICS INTERNAL ENERGY
Finally, if put in terms of specific units, we get:
du = dh dw
or
a general form of the 1st Law of Thermodynamics that we will use:
dh = du + dw (Eq 6.2)
12. FIRST LAW OF THERMODYNAMICS
CONSTANT VOLUME AND CONSTANT PRESSURE SPECIFIC HEAT CAPACITIES
Recall Table 5.1 which listed some specific heat values of different substances. Why were no gases included in that list?
The reason is that the heat required to warm 1 gram of any particular gas 10C will vary depending on how much the gas volume is allowed to expand as a result of the heating.
13. FIRST LAW OF THERMODYNAMICS CONSTANT VOLUME AND CONSTANT PRESSURE SPECIFIC HEAT CAPACITIES
If the gas volume is kept constant, all the heat added is used solely to increase the temperature. If we allow volume to expand so that pressure remains unchanged, the heat added would have to contribute to both increasing the temperature plus doing work (expanding the volume: dw = pd?).
14. FIRST LAW OF THERMODYNAMICS CONSTANT VOLUME AND CONSTANT PRESSURE SPECIFIC HEAT CAPACITIES
So, which value is larger, cv, or cp? Why
These specific heat capacities are represented as:
specific heat capacity = cv = dh |
at constant volume dT |V (Eq 6.3)
specific heat capacity = cp = dh |
at constant pressure dT |p (Eq 6.4)
INTERNAL ENERGY OF AN IDEAL GAS
In addition to an ideal gas satisfying the Equation of State for all temperatures and pressures, an ideal gas is also is also one in which the internal energy is a function of temperature only. In other words, any heat added (at constant volume) affects only the random molecular motions (hence temperature increase). The formula for the specific internal energy of an ideal gas is:
du = cvdT (Eq 6.5)
Real gases (as opposed to ideal gases we have been talking about) must take into account overcoming intermolecular forces in addition to increasing kinetic energy.
DIFFERENT FORMS OF THE 1ST LAW OF THERMODYNAMICS
We now know a basic form of the 1st Law to be:
dh = du + dw.
Since we have already shown that for an ideal gas:
du = cvdT, and
dw = pd?,
we may write the 1st Law as:
dh = cvdT + pd? -------------- > explicit form (Eq 6.6)
Because d? is not an incremental value commonly measured by meteorologists, another more "meteorologically-friendly" form is:
dh = cpdT - ?dp -------------- > implicit form (Eq 6.7)
Note that the incremental values dT and dp can be measured by the common weather instruments -- the thermometer and the barometer.
(The derivation of the implicit form can be found in Appendix C).
The term cpdT is the specific enthalpy, or sometimes referred to as the sensible heat. In the implicit form, it is important to realize that cpdT is not the specific internal energy, and ?dp is not the specific work.
15. FIRST LAW OF THERMODYNAMICS CONSTANT VOLUME AND CONSTANT PRESSURE SPECIFIC HEAT CAPACITIES
For dry air, accepted values of cv and cp are:
cv = 717.6 J/(kg C) = 0.171 cal/(g C)
cp = 1004.6 J/(kg C) = 0.240 cal/(g C)
16. FIRST LAW OF THERMODYNAMICS INTERNAL ENERGY OF AN IDEAL GAS
In addition to an ideal gas satisfying the Equation of State for all temperatures and pressures, an ideal gas is also is also one in which the internal energy is a function of temperature only. In other words, any heat added (at constant volume) affects only the random molecular motions (hence temperature increase).
17. FIRST LAW OF THERMODYNAMICS INTERNAL ENERGY OF AN IDEAL GAS
The formula for the specific internal energy of an ideal gas is:
du = cvdT (Eq 6.5)
Real gases (as opposed to ideal gases we have been talking about) must take into account overcoming intermolecular forces in addition to increasing kinetic energy.
18. FIRST LAW OF THERMODYNAMICS DIFFERENT FORMS OF THE 1ST LAW OF THERMODYNAMICS
We now know a basic form of the 1st Law to be:
dh = du + dw.
Since we have already shown that for an ideal gas:
du = cvdT and dw = pd?
19. FIRST LAW OF THERMODYNAMICS DIFFERENT FORMS OF THE 1ST LAW OF THERMODYNAMICS
(Eq 6.6) dh = cvdT + pd? ------> explicit form
Since d? is not commonly measured by meteorologists, another more "meteorologically-friendly" form is:
(Eq 6.7) dh = cpdT - ?dp ------> implicit form
20. FIRST LAW OF THERMODYNAMICS DIFFERENT FORMS OF THE 1ST LAW OF THERMODYNAMICS
(Eq 6.7) is called the meteorologically-friendly
form of the First Law because it uses dT and dp (T and p are routinely measured quantities).
(The derivation of the implicit form can be found in Appendix C.)
21. FIRST LAW OF THERMODYNAMICS DIFFERENT FORMS OF THE 1ST LAW OF THERMODYNAMICS
.
In (Eq 6.7), the term cpdT is called specific enthalpy, or sensible heat. In the implicit form, it is important to note that cpdT is not the specific internal energy and ?dp is not the specific work.
