First law of thermodynamics
Kinetic energy:
mv 2
K=
2
Potential energy (U):
Conservation of energy in mechanics:
mechanical energy of a closed system is conserved
!K + !E p = 0
E p = mgh
External forces and work they do.
!K + !E p = Wext
work of the external forces
The system is NOT totally on its own (not closed or isolated).
External forces can do work on it and the system can do work
on external objects.
"K + "E p = Wext ! Wsys
Wsys is the work done by the system (in
this case – against friction forces).
If Wsys > 0 the energy decreases.
"K + "E p = Wext ! Wsys
1st law of thermodynamics.
In thermodynamics we introduce a new type of energy – internal
energy of the system, U, which is a sum of energies of
microscopic components of the system, e.g., gas molecules.
"K + "E p + "U = Wext ! Wsys
In thermodynamics, we usually assume that kinetic and potential
energy of the system do not change, or their changes are
negligible:
!K + !E p = 0
"U = Wext ! Wsys
We unify Wext and Wsys by introducing the work W, which is positive
if done by the system and negative if done by external forces
"U = !W
1st law of thermodynamics.
We unify Wext and Wsys by introducing the work W, which is positive
if done by the system and negative if done by external forces
"U = !W
How do we convert work into internal energy? This is easy!
"U = !W
External work done by the
hands (negative W ) is
converted into positive internal
energy (positive ΔU)
Potential energy of the weights
is converted into work (external
work, negative W ) and into an
increase in the internal energy
of water (positive ΔU )
Are not we forgetting something, though?
In order to increase the internal energy of a system, we do not
necessarily need to do some work on it. There is a simple and common
alternative – transferring heat, Q, from some hot object (heater):
"U = Q ! W
The heat Q is positive if the energy is transferred to the system.
First law of thermodynamics
"U = Q ! W
change in the internal
energy of the system
net heat
transferred
to the system
work done
by the system
The change in the internal energy of a system depends only on the
net heat transferred to the system and the net work done by the
system, and is independent of the particular processes involved.
The equation is deceptively simple… One of the forms of the general
law of conservation of energy. BUT!
Mind the sign conventions,
prepositions and
multiple meanings/implications!
Heat is energy in transit!
Internal energy relates to the energetic
content of an object or a system.
Whereas Heat is energy in transit!
"U = Q ! W
change in the internal
energy of the system
net heat
transferred
to the system
work done
by the system
The heat, Q is considered positive, when it is transferred
TO the system. – The system gains internal energy.
The work, W, is considered positive if it is done BY the system.
– The system loses internal energy.
WHY? – The history heavily influenced by the heat engines.
"U = Q ! W
change in the internal
energy of the system
net heat
transferred
to the system
work done
by the system
Statement #1 – conservation of energy
The energy is transferred to and from the system by means of
heat transfer and mechanical work.
It causes change in the energetic content of the system – its
internal energy. The total amount of energy is conserved, though.
"U = Q ! W
change in the internal
energy of the system
net heat
transferred
to the system
work done
by the system
Implication: both heat, Q, and mechanical work, W, are means of
energy exchange between the system and the outside world.
The both are kinds of energy in transit. That’s why they are on
the same side in the equation.
Nevertheless, the heat, Q, specifically relates to the energy
transferred due to temperature difference alone. While, W,
incorporates all other sorts of energy transfer, most commonly
mechanical work.
"U = Q ! W
change in the internal
energy of the system
net heat
transferred
to the system
work done
by the system
Sometimes things may become confusing: solar heaters vs.
solar batteries.
We will try to restrict ourselves to unambiguous situations…
Mechanical work is rather simple and straightforward.
"U = Q ! W
change in the internal
energy of the system
net heat
transferred
to the system
work done
by the system
Consequence: heat, Q, and mechanical work, W, are interchangeable
in terms of their effect of internal energy of the system…
"U = Q ! W
change in the internal
energy of the system
net heat
transferred
to the system
work done
by the system
Statement #2 – internal energy, U, is a function of internal
state of the system, a thermodynamic state variable –
a quantity, whose value does not depend on how a system got to a
particular state.
In principle, you can measure internal energy of the system -, by
measuring the sum of energies of all molecules, - the same way as you
can measure its temperature and pressure – both the state variables,
well defined in thermodynamics equilibrium.
Usual ambiguity with setting the zero level of energy, though…
What is energy of Uranium at absolute zero temperature?
NET heat
dU dQ dW
=
!
dt
dt
dt
transferred
to the system
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 car’s 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?
Let’s see what happens within 1 sec:
"U = Q ! W
!U = ?
Q=?
W =?
Let’s see what happens within 1 sec:
!U = ?
"U = Q ! W Q = ?
W =?
1. 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 ΔU = 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 = Q1+Q2+Q3= 59 kJ.
3. Total work, by 1st law: W = Q – ΔU = 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.
First law of thermodynamics
!Etotal = !K + !E p + !U =
= Q !W
change in the total
energy of the system
net heat
transferred
to the system
work done
by the system
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 ΔK and ΔEp are equal to zero and we end up with:
"Etotal = "U = Q ! W
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…
PV = nRT
"U = Q ! W