Download THERMAL ENERGY AND OTHER TYPES OF INTERNAL ENERGY

THERMAL ENERGY AND OTHER TYPES OF INTERNAL ENERGY
1] FRICTION AND THERMAL ENERGY
- Until this section, all mechanics is based on the model of object as a single material point. In reality, the
objects (i.e. system components) are constituted by atoms and molecules which “interact between them and
move inside the object” and this means some “energy inside the object”. Molecules are strongly bound
inside a solid, slightly bound inside a liquid and free in a gaz. But, no matter what is the physical state of
object, molecules are in a continuous random motion. This motion means some average speed and this is
associated by a kind of kinetic energy inside the object. When this type of kinetic energy increases, the
temperature of object increases, too. The temperature of the object is a macroscopic parameter related to
the average kinetic energy of microscopic particles inside it. One say that, there is a thermal energy Eth
inside any object. In the following, one refers to a system constituted by objects with microscopic structure
and derives a conservation low based on parameters work, mechanical energy and thermal energy.
-The experiments show that the friction produces heat and when the work by friction produces only heat,
the increase of thermal energy of objects that rub on each other is
ΔEth ( > 0)= −𝑾𝒇 = f*d
(1)
If the friction is one of several external forces acting on the system, one may put aside the (negative) work
by friction in the expression of energy conservation principle and get Wext_net = Wext + Wf = ΔEmech (2)
Then, Wext = ΔEmech - Wf = ΔEmech + ΔEth and finally rewrite the principle of energy conservation as
Wext = ΔEmech + ΔEth
(3)
-Note that Wext in this expression does not include the work by friction. So, the external work without
friction work goes for the change of total mechanic energy and the change of thermal energies of the
system ΔEth-sys and that of the objects that rub with its parts ΔEth-obj.
ΔEth = ΔEth-sys + ΔEth-obj
(4)
Wext
Fig.1
ΔEmech
ΔEth
ΔEmech + ΔEth
Wext
Fig 2
One may include into system the “adjacent objects affected by friction” and make the friction an internal
non-conservative force of system. Then, the expression (3) would tell that net work provided by all external
forces (friction is not any more external) goes to change the mechanical and thermal energies of the system.
Example: A block with mass m=10kG moving with speed υ1 = 5m/s on a horizontal frictionless plane
stops at distance “d” once it gets over another plane acting on it with friction force f k = 5N .
d
a) Find the change of thermal energy ΔEth of block - plan set
b) Find “d”
If one sees the words temperature or thermal one must figure out that one has to consider the friction as
an internal force and refer to the principle energy form (3) that contains the thermal energy.
By excluding the friction from external forces one get Wext = 0 . Then, the equation (3) gives
ΔEmech + ΔEth = Wext = 0
So, a) ΔEth = Eth2 – Eth1 = 125 J
and
and
[(0 + mgh) – (10*25/2 + mgh )] +[( Eth2- Eth1)] = 0
b) ΔEth =|𝑾𝒇 |= f*d i.e. 125 = 5*d so
d = 25m
Important: If the heat or thermal energy is not required one refers to a system where the friction is an
external force and uses the principle of mechanic energy conservation for a material point model.
Wext_net = ΔE = Emech_2 – Emech_1 = (K2 +U2) – (K1+ U1) = ΔK + ΔU
(5)
But, if the thermal energy is required one must refer to the total (mechanic + thermal) energy of system
Emech = U + K+ Eth and apply the principle of energy conservation in the form
Wext = ΔEmech + ΔEth = [(K2 + U2 ) – ( K1+ U1)] +[ Eth2 – Eth1] = ΔK+ΔU+ ΔEth
(6)
Important: The experiments show that K and U can transform completely into each other or into Eth
but Eth cannot transform completely into K or U. A disorganized motion cannot be converted naturally
(by itself) into an oriented motion. Ex: A hot block cannot start moving along one direction just because
its temperature decreases. That’s why the thermal energy is not considered as a pure mechanical energy.
Also, one uses “calorie” a particular unit to measure heat i.e. the thermal energy. (1 cal = 4.186 J)
2] OTHER TYPES OF INTERNAL ENERGY
-Consider an exothermic chemical reactions inside an sealed container; the molecules of a sample A
interact chemically with molecules of a sample B at room temperature and produce molecules of the sample
A-B with higher temperature (ΔEth > 0). It may be produced even an explosion (sample particles get very large
kinetic energy and break container) . As the system of two samples (A, B) is isolated (Wext= 0), the principle of
energy conservation (3) would tell that ΔEmech + ΔEth = 0 but the experiment shows that ΔEmech > 0 and
ΔEth > 0 that is ΔEmech + ΔEth > 0 . This contradiction is solved easily by accepting that there is a molecular
energy inside each of the molecules of two samples. Their sum over all the molecules in the sample, Emol
remains unchanged as long as there is no chemical reaction. So, the total energy of sample is
Etot = Emech + Eth + Emol
(7)
Then, the principle of energy conservation for an isolated system would be written ΔEtot = Wext = 0
ΔEmech + ΔEth + ΔEmol = 0 and ΔEmech + ΔEth = - ΔEmol > 0 because ΔEmol = Emol-2 - Emol-1 < 0 as the
molecular (or chemical) energy of the system is decreased . This means that the amount of energy lost by
Emol is transformed into mechanical and thermal energy of the system “which are increased”.
-In a battery, the molecular energy is transformed (via a chemical reaction) into electrical energy Eelect which
is another type of internal energy. There is a set of other internal energies (Estruct in a solid or liquid structure,
Eat - atomic energy inside the atoms, Enucl nuclear energy inside the nuclei and Erad radiation energy) which
cannot transform completely and naturally into pure mechanic energy (K or U). So, they are all nonmechanical forms of energy. If one group all them into a single term Eint (internal energy), one gets
Eint = Eelectr + Estruct + Emol + Eat + Enucl + Erad
and the total energy of an object can be expressed as
Etot = Emech + Eth + Eint
(8)
(9)
3] GENERAL PRINCIPLE OF ENERGY CONSERVATION
The results of multiple experiments confirm the following:
- If one includes inside a system all the objects that may affect each other, one creates an isolated system.
The total energy of an isolated system remains constant in time i.e.
ΔEtot = ΔEmec + ΔEth + ΔEint = 0
(10)
Note: This does not exclude motion and energetic exchanges inside the system; but if they happen, the
energy is transformed from one form to another form in such a way that their sum remains unchanged.
- If the system is not isolated the amount of energy that it exchanges with adjacent space regions Eexchange,
is equal to the change of its total energy
ΔEtot = Etot-2 – Etot-1 = Eexchange
(11)
If the system exchanges only work, then Eexchange = Wext and Wext = ΔEmech + ΔEth + ΔEint (12)
Remember:
*The total energy of system increases if Wext > 0 and decreases if Wext < 0).
* The work by friction is not included into Wext at expressions (3, 6, 10, 12).
*The total energy conservation principle (12) transforms into form (3) when ΔEint = 0.