Law of Thermodynamics

Prof. Lukas Mltner | Mechatronics | Engineering Thermodynamics - VO

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Lecture

Engineering Thermodynamics 0th and 1st law of thermodynamics,

Enthalpy and heat capacities

Prof. DDI Dr.techn. Lukas Mltner


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Overview

The zeroth law of thermodynamics

The first law of thermodynamics

- Work on closed systems

- Work on open systems

Thermodynamic description of states

- Enthalpy

- Heat, heat capacities and temperature


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The first equilibrium postulate

Existence of an equilibrium state

Each single system without any external influence and of ordinary sizes strives to a

equilibrium state, determined by the boundary conditions.


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The second equilibrium postulate

Transitivity of thermal equilibria

If two systems in a thermal equilibrium are in touch with a third system, so the third system

must be in equilibria with the other two systems. Systems in thermal equilibrium have the

same temperature.


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Overview






- Enthalpy



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Each system has a state variable called energy. It is constant for a closed system.


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Equivalence principle and energy conservation


generally expressed:

expressed for a not-moving system:

Heat and work are forms of energy.


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Equivalent formulations of the first law


Heat is a form of energy

Energy can neither be destroyed nor generated, but most converted

A machine can only perform work when her the same amount of energy is supplied

According to the first law heat and work are equivalent when it comes to change the energy

of a system.

You can increase the temperature of a system by work alone. In addition, the temperature

rise will always be the same, regardless of the kind of work (compression, electric heating,

...).


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If the energy of a system increases by applying work or heat, these will be set with a positive prefix. An example: Some work is applied to the system, if some water is pumped up to the water reservoir of a water power plant. Performs this system some work by converting potential energy to electric energy, the water reservoir loses the same amount of energy and the prefix was negative.

To spend the formulation dU = dq + dw wisely we must derive dq and dw from operations

from the surroundings.


Prefix convention


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Overview






- Enthalpy



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Work on closed systems

Volume change work

Types of energy on a closed system:

p,V work

Heat

Dissipation

All of these forms of energy contribute to the internal energy U stored in the system.


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p,V work


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Splitting of the volume change work

Displacing work Wu12

From the constant ambient pressure pb for

displacing the piston applied work (and thus

supplied to the system).

Effective work Wn12

The work of the piston rod (after deduction of

the ambient pressure pb) supplied to the

system.


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Dissipation Wdiss12, heat Q12 and internal energy U


Dissipation energy Wdiss12

Devaluation of the supplied energy by friction, throttling, mixture, etc.

Heat Q12

The energy that occurs due to the temperature difference to the environment via the

system boundaries (for a system with non-adiabatic system boundaries)

Internal energy U

The energy saved in the system:

kinetic energy (proper motion) of molecules potential energy (chemical/physical binding energy)

The internal energy is a caloric state variable!


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Dissipation in detail:


Dissipation energy can only be applied to a system it is always positive!

The necessary work for a compression increases with dissipation,

the performed work at an expansion decreases with dissipation.


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Change of the internal energy U


The energy stored in the system (internal energy) is changed in a closed system by

applying heat Q12, volume change work WV12 and dissipation energy Wdiss12.


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State variable or process variable - repetition


The internal energy U is a state variable of the system and therefore in each state (1

before, 2 after the process) defined. Its change due to a process is:

Heat, volume change work and dissipation are process variables:

Since they are defined only as a process variable during the process (1 to 2), or through

the process, it only makes sense to use them as exchange sizes (1 to 2) and not as

properties!


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Overview






- Enthalpy



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Types of energy

Work on open systems

In open systems following types of work can be performed or applied:

Volume work

Technical work (reversible)

Dissipation (friction, throttling,)

Change of potential and kinetic energy


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Free expansion (dV):

When a gas flows against an external pressure pa = 0, no work is done because there is no opposing force.

pa = 0 dw = padV = 0

Expansion against constant pressure (dV):

The gas expands until it is stopped mechanically, or if pi = pa. A typical example would be the expansion of a gas to the atmosphere.

dW = padV

The work between the volume Va and Ve is

w = pa V


Volume work


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Dissipation


Some work can be applied to a system without a

volume change, e.g. by the dissipative effects of

a rotating propeller

In this case, the work is converted to heat due to friction. Friction work can only be fed to

the system. The friction work is therefore always positive. The process can not be reversed,

so it is irreversible.

Further types of work

Furthermore work in the form of electric and magnetic energy etc. can be applied. However,

these works play no role in most thermodynamic processes. They can be supplied also

reversible (e.g. charging a battery) or irreversible (e.g. ohmic resistance).


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Work on (open) systems

Arbeitsart W Q U T

Expansion against vacuum

1. isothermal 0 0 0 0

2. adiabatic 0 0 0 0

Expansion against p=const.

1. isothermal -paV paV 0 0

2. adiabatic -paV 0 -paV paV/cv

Reversible expansion

1. isothermal -

nRT*ln(VE/VA) nRT*ln(VE/VA) 0 0

2. adiabatic cVT 0 CVT (T1 *((V1/V2)

n-

1)-T2

Conclusion of work, heat and internal energy


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Overview






- Enthalpy



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Enthalpy

The enthalpy includes in addition to the internal energy U (= thermal energy by means of

random motion of the particles and the resulting friction) the volume work which is (was)

required to make space in its environment.

Evaporation of water:

1 kg 1,6 m3

1 kg 1 dm3

pamb , V2

pamb , V1


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Enthalpy

m1, p1, V1, U1 m2, p2, V2, U2

Example compression:

Wzu


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Log(p), h-diagram

lo

g p

[P

a]

wet steam superheated

steam

Saturated

steam

supercooled

liquid

Critical point

T = const

T = const


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Log(p), h-diagram


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Log(p), h-diagram (water)


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Log(p), h-diagram (134a)


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Overview






- Enthalpy



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If some heat is conducted to material its temperature will change. The quantity of this

temperature change depends on the conditions (e.g. isochoric, isobaric,)

For a limited temperature range, the connection can be represented as follows:

q = c T

Material absorbes heat and the change of temperatur can be measured.

c = amount of heat / temperature difference

However, this applies only if all of the heat is also used to change the temperature!

If the material expands ist volume during heat input V will takes place presure volume work is conducted w = p V!

A part of the supplied work is converted to work a sharper delineation of this definition is needed!

Heat, heat capacities and temperature

Zusammenhnge


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If a change of the volume not possible the process takes place under isochoric condition the whole amount of heat increases the internal energy. W = p V = 0

dq = cvdT Index v represents an isochoric process.

q = cvT if cv can be assumed to be constant over the temperature range considered.

If no work is done (neither labor nor any other volume), then:

du = dq + qw du = dq du = cvdT

This definition allows to calculate the change of the internal energy at isochoric heat supply or

dissipation.

Many processes take place under isobaric conditions instead of isochoric (e.g. open chemical

reactors). The result is, that pressure volume work occurs simultanous and increases the heat

capacity

dq = cpdT



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Isobaric heat exchanges are described by the enthalpy.

du = cpdT or if cp = const. H = cpT

With the isobaric and isochoric heat in a system we have the possibility to calculate H and U. The correlation between enthalpy and internal energy is:

H = U + pV

oder H = U + nRT

The temperature is raised for dT:

dH = dU + nRdT

dh = cpdT und du = cvdT

cpdT = cvdT + nRdT

cp = cv + nR

cp - cv = nR oder or molaric: cp,m cv,m = R


Correlation between heat capacities and enthalpy

for german native speakers only


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Law of Thermodynamics

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