ESCI 341 –
Atmospheric Thermodynamics
Lesson 3 – The
First Law of Thermodynamics
References: An Introduction to Atmospheric Thermodynamics, Tsonis
Introduction to Theoretical Meteorology, Hess
Physical Chemistry (4th edition), Levine
Thermodynamics and an Introduction to Thermostatistics, Callen
Reading: Tsonis, Sections 4.1
thru 4.3
THE LAWS OF THERMODYNAMICS
l Thermodynamics
can be summed up in several “laws.”
These laws are:
o
Zeroth law – if two systems are each
separately in equilibrium with a third system, then the first two systems are
also in equilibrium with each other
o
First law – energy is conserved
o
Second law – In an isolated system entropy
never decreases.
o
Third law – entropy is zero at
absolute zero
l The
“laws” are actually postulates that have been found to hold true.
l We
will see later that the second law implies that energy cannot be converted to
work with 100% efficiency.
l For
the thermodynamics of the atmosphere we will be concerned mostly with the first
and second laws.
THE FIRST LAW OF THERMODYNAMICS
l The
first law of thermodynamics expresses the conservation of energy. It is given as
.
l The
first law states that internal energy can be changed either through heating or
through work.
l Using
intensive properties, the first law becomes
.
l Our
convention will be that heat added to the system and work done on the system
will be positive.
o
Thus, work done by the system on its
surroundings will be negative.
P-V WORK
l Work
is defined as force acting over a distance,
.
l If
a gas expands quasi-statically against a pressure, p, the work
done by the gas is given by the pressure multiplied by the change in volume, V,
or
.
o
This definition of work is only valid if the
process is quasi-static, so that the system remains in equilibrium throughout
the process.
o
The negative sign is included because work is
being done by the system.
l The
first law is then written
, (1)
o
In terms of specific quantities, the first
law is
,
where a
is the specific volume (V/m, or r -1).
NOTE:
In the “old days” it was conventional to define positive work as work
done “by” the system, so that the first law would be dU = dQ - dW, and dW = pdV. Modern convention is to
define positive work as work done “on” the system, so that dU = dQ + dW and dW = -pdV. Either
convention leads to the correct form of expression (1), so it really doesn’t
matter. But, keep in mind that Tsonis’ textbook uses the older definition for work, and
differs from what we use in this class.
l The
first law in this form tells us that if a gas expands then its internal energy
must either decrease, or heat must be added to it in order to keep the internal
energy from decreasing.
o
In an adiabatic process, no heat is added or
subtracted. Therefore dq = 0. this
means that if a gas expands adiabatically its internal energy (and hence, its
temperature) will decrease.
EXERCISES
1.
Prove that for a volume of arbitrary shape that the work done in
expanding the volume by a differential volume, dV, is pdV. Hint: Imagine every where on the surface of the
volume that the surface is pushed out an amount 
, where 
is a vector whose
direction is everywhere normal to the surface.
2.
a. What is the minimum amount of
work done by you in blowing up a spherical party balloon to a diameter of 8
inches? Assume standard sea-level
pressure.
b.
Why is this the minimum amount of work?