Thermal and Other Types of Internal Energy

Kreshnik Angoni

FRICTION AND THERMAL ENERGY

- Till here we neglect that objects (system components) are constituted by atoms and molecules which “interact and move inside the object” and this means some “energy inside the object”.

Molecules and atoms are strongly linked inside a solid, slightly linked inside a liquid and free in a gaz. But, no matter what is the physical state of object, they are in a continuous random motion in space.

This motion means some average speed and this means some average kinetic energy. When this energy is considerable the object has high temperature. The temperature of the object is a macroscopic parameter related to the microscopic average kinetic energy of particles inside it. In energy terms, we say that, there is a thermal energy $E_{th}$ inside any object.

-The experiments have proven that the magnitude of work by friction goes completely to increase the thermal energy of two objects that rub on each other, i.e.

$\left|W_{f}\right|=f*d=E_{th2}-E_{th1}=\Delta E_{th}$ ......(1)

If the friction is one of external forces acting on the system, one may put aside the (negative) work by friction in the expression of energy conservation principle and get

$W_{ext-net}=W_{ext}+W_{f}=\Delta E_{mech}\,\!$ .......(2)

Then,

$W_{ext}=\Delta E_{mech}-W_{f}=\Delta E_{mech}+|W_{f}|\,\!$ and finally

$W_{ext}=\Delta E_{mech}+\Delta E_{th}\,\!$ ....... (3)

-Note that $W_{ext}$ in this expression does not include the work by friction.

The expression (3) tells that the external work can go for the change of pure mechanic energy and thermal energy of a system.

Example: A block with mass m = 10kg moving with speed $v_{1}$ = 5m/s on a horizontal frictionless plane stops after distance “d” when moving on a surface with friction where f = 5N.

a) Find the distance “d”.

1) Apply the work-energy theorem ; $W_{net}=W_{f}=K_{2}-K_{1}\,\!$; i.e.-5*d = 0 – 10*$5^{2}\,\!$/2 and d = 125/5 = 25m 2) Apply the principle of mechanical energy conservation (10) for earth - block non-isolated system

(state_1)$E_{1}=K_{1}+U_{1}\,\!$ = (10*$5^{2}\,\!$)/2 + $mgh_{1}\,\!$ ;

(state_2) $E_{2}=K_{2}+U_{2}=0+mgh_{2}=mgh_{1}\,\!$;

“Friction external force” . So, $E_{2-mech}-E_{1-mech}=W_{ext-net}=W_{f}\,\!$ = -5*d

[(0-125)+( $mgh_{2}-mgh_{1}\,\!$)] = - 5*d and d=125/5=25m

b) From the experience, we know that the temperature of block and the plan increases. Another way of asking questions on this example is:

b-1) Find the increase of thermal energy of block - plan system then

b-2) Find “d” by using the change in thermal energy when the block is stopped.

If we see the words temperature or thermal we must figure out that we have to exclude the friction from external forces and refer to the principle energy form containing the thermal energy. For this system:

- The friction work is not part of external work and $W_{ext}=0\,\!$ (Isolated system)

-The principle of mechanic energy conservation tells that

$\Delta E_{mech}+\Delta E_{th}=W_{ext}=0[(0+mgh)-(125+mgh)+(E_{th2}-E_{th1})]=0\,\!$

So,

b-1)$E_{th2}-E_{th1}=125J\,\!$ and

b-2) $\Delta E_{th}$ = f*d i.e. 125 = 5*d and d = 25m

Remember: If the heat or thermal energy is not mentioned one refers to a system where friction is external force and uses the principle of mechanic energy conservation in its simple form.

$W_{ext-net}=E_{mech2}-E_{mech1}=[K_{2}+U_{2}]-[K_{1}+U_{1}]\,\!$ .......(4)

But, if the thermal energy is required one must refer to the total mechanic + thermal energy of system

$E_{mech}=U+K+E_{th}\,\!$ and apply the principle of energy conservation in the form

$W_{ext}=\Delta E_{mech}+\Delta E_{th}=[(K_{2}+U_{2})-(K_{1}+U_{1})]+[E_{th2}-E_{th1}]\,\!$......(5)

Important Note: The experiments show that K and U can transform completely into each other or into $E_{t}h\,\!$ but $E_{t}h\,\!$ 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. In general, one uses “calorie” a particular unit to measure heat. (1 cal = 4.18 J)

OTHER TYPES OF INTERNAL ENERGY

-In exothermic chemical reactions, the molecules of a sample_ A interact with molecules of a sample_ B at room temperature and produce molecules of the sample A-B with higher temperature (may be even an explosion i.e. high kinetic energy of particles).

As the system of two samples (A, B) is isolated, the principle of energy conservation would tell that

$\Delta E_{mech}+\Delta E_{th}=0\,\!$ but the experiment shows that $\Delta E_{mech}+\Delta E_{th}\,\!$ > 0.

This contradiction can be solved easily if we consider that there is a molecular energy $E_{mol}$ inside the molecules of two objects which remains unchanged as long as there is no chemical reaction.

So, the total energy of two samples is $E_{tot}=E_{mech}+E_{th}+E_{mol}\,\!$.

Then, the principle of energy conservation for an isolated system would be written

$\Delta E_{mech}+\Delta E_{th}+\Delta E_{mol}=0\,\!$ and $\Delta E_{mech}+\Delta E_{th}=-\Delta E_{mol}\,\!$ > 0 because $\Delta E_{mol}=E_{mol-2}-E_{mol-1}\,\!$ < 0

which explains that the molecular (or chemical energy) is decreased and transformed into mechanical and thermal energy of the system.

-In a battery the molecular energy is transformed (via chemical reaction) into electrical energy$E_{el}\,\!$ which is another type of internal energy.

There is a set of other internal energies( $E_{struct}\,\!$ in a solid or fluid structure, $E_{at}\,\!$ atomic energy inside the atoms, $E_{nucl}\,\!$ nuclear energy inside the nuclei and $E_{rad}\,\!$ radiation energy) which cannot transform completely and naturally into pure mechanic energy (K or U).

So, they are all non-mechanical forms of energy. If we group all them into a single term E_{int} , we get

$E_{int}=E_{el}+E_{struct}+E_{mol}+E_{at}+E_{nucl}+E_{rad}\,\!$ ...... (6)

and the total energy of an object can be expressed as:

$E_{tot}=E_{mech}+E_{th}+E_{int}\,\!$ ...... (7)

GENERAL PRINCIPLE OF ENERGY CONSERVATION

The results of many experiments show that:

- If we include inside a system all the objects that can affect each other, we create an isolated system. The total energy of an isolated system remains constant in time i.e.

$\Delta E_{tot}=\Delta E_{mech}+\Delta E_{th}+\Delta E_{int}=0\,\!$ .......(8)

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 in such a way that their sum remains unchanged.

- If the system is not isolated the amount of energy it exchanges with adjacent space regions E_{exchange}, is equal to the change of its total energy

$\Delta E_{tot}=E_{tot-2}-E_{tot-1}=E_{exchange}\,\!$ ......(9)

If the system exchanges only work, then$E_{exchange}=W_{ext}\,\!$ and $W_{ext}=\Delta E_{mech}+\Delta E_{th}+\Delta E_{int}\,\!$......(10)

Remember:

• The positive work done by forces outside system ( $W_{ext}\,\!$ > 0) increases the total energy of system.
  
• The negative work done by forces outside system ( $W_{ext}\,\!$ < 0) decreases the total energy of system.
  
• The work by friction is not included into $W_{ext}\,\!$ at expression (10).
  
• The total energy conservation principle (10) transforms into (3) when $\Delta E_{int}=0\,\!$.
  
  

-A “source” can transfer different types of energy (work, heat, irradiation, electric..), to the adjacent regions of space. So, the general expression for the delivered power [watt] from a “source” must take into account all the possible energy transfers in “ a second”

$P=-{\frac {dE}{dt}}\,\!$ ......(11)

where E [joule] stands for the total energy(all type included) of the “source” that delivers energy.

The work done by the source is a portion of energy transferred from the “source” to the adjacent regions. So, the delivered mechanic power is only one of the components of expression (11).

If only the mechanical energy of “source” changes during the time it produces work then the delivered mechanical power [watt] is due to only mechanical changes of energy.

Note: The sign “ - “ in expression (11) is related to the fact that the energy of the source is decreased when providing power while this power is positive in the sense that the force originated from the system does positive work.