First law of thermodynamics

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First law of thermodynamics
In the usual case our system is an ideal gas
under a piston It does not move, - so there is
no change in either kinetic or potential
energy. Therefore, the terms DK and DEp are equal
to zero and we end up with
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Continuous processes we differentiate with
respect to time to define rates of energy flow,
measured in Watts.
Gasoline burning in an automobile engine
releases energy at a rate of 160 kJ per second.
Heat is exhausted through the cars radiator at
a rate of 51 kJ per second and out of the exhaust
at 50 kJ per second. An additional 23 kJ per
second goes to frictional heating within the
machinery of the car. What fraction of the fuel
energy is available for propelling the car?
Lets see what happens within 1 sec
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Lets see what happens within 1 sec

• Our system of interest is the engine itself. We
• assume that it is well warmed up, and the car is
  cruising.
• So the thermodynamic state of the engine does not
  change and DU 0.

2. Heat balance. (a) Obtained from burning the
gas Q1 160 kJ. (b) Lost through the radiator
Q2 -51 kJ. (c) Lost through the exhaust Q3
-50 kJ. The total balance of heat Q
Q1Q2Q3 59 kJ.
3. Total work, by 1st law W Q DU Q 59
kJ. Where does this work go?
It is supplied to some external object/system.
What is it?
It is the machinery of the car, which is a
system external to the engine. Out of the 59 kJ
it gets, 23 kJ is wasted into heat through
friction, and the remaining 36 kJ are supplied to
the driving wheels.
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Thermodynamic processes
We are interested in changes in internal energy,
the heat transferred to or from the system and
the work done by the system - ideal the gas
under piston
In principle, all we need to know are the ideal
gas law and the 1st law of thermodynamics
BUT There are many, processes, conditions
(idealistic or realistic) and applications
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Thermodynamic processes in ideal gas
Usually presented as P-V diagrams
A diagram suggests that both pressure and volume
are well defined in every point.

• The gas is in a thermodynamic equilibrium in
  every point, every moment of time
• We call that a quasi-static process.

Equilibrium with what?..
At least with itself! That is, different parts
of the gas are in equilibrium with each other.
Can be implemented if we change things slowly.
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Quasi-static processes.
Heating and boiling water on a stove.
Quasi-static? Why?
The least we can say is that the water is in
contact with burning gas from below and cool air
from above. So, its temperature is not likely
to be the same at the top and bottom, which
precludes thermodynamic equilibrium and
quasi-static process.
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Quasi-static processes.
Is this one any better?
Practically, how slowly you should go to be
quasi-static?
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Quasi-static processes are in principle
reversible
You can go back and forth along the same line of
well defined equilibrium states.
Can there be multiple paths to get from 1 to 2?
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Work done and heat transferred our major
concerns!
Work done by the gas
P pressure of the gas Dx displacement of
the piston, A area of the piston
The work is positive when the gas expands!
Differential form
Integral form also good for varying pressure
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Work done and heat transferred our major
concerns!
Work done by the gas
P (varying) pressure of the gas dV
differential volume change
P
V
Work, W, - area under curve on a P-V diagram
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Multiple ways to get (quasi-statically !) from an
initial to a final state
Is work going to be the same for different
processes?
NO!
NO!
Is heat going to be the same?
Is the change in internal energy going to be the
same?
YES!
Internal energy is a function of state and will
be the same as well as it variation between the
states.
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Isothermal process T const
Isotherm
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Constant volume (isochoric) process V const.
n number of moles of the gas Cv molar
specific heat at constant volume heat capacity
of one mole of the gas in an constant volume
process.
(Compare with )
Why bother introducing a new parameter?
Measuring Cv we learn about internal energy of
the gas as a function of temperature!
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Isobaric processes P const.
P
V
Since the pressure of the gas remains constant,
calculation of the work done by the gas is
particularly simple.
What about internal energy and heat?
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What about internal energy and heat?
P
V
From the 1st law and equation for Cv
Ideal gas at constant pressure
Molar specific heat at constant pressure
(definition)
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What about internal energy and heat?
P
V
From the 1st law and equation for Cv
Molar specific heat at constant pressure
(definition)
Why is specific heat at constant pressure higher
than at constant volume?
Heat capacity is defined as, CQ/DT. It depends
on heat transferred to the system, NOT on the
change in the internal energy. Therefore, heat
capacity is a function of the process and is
different for different processes.