THERMODINAMICS

Tóth Mónika 2012. 28-29.11.

monika.a.toth@aok.pte.hu

Temperature

Temperature: is related to the average

energy of the motion of the particles of an

object or system.

SI unit of temperature: Kelvin (K) 0 oC=273,15 K

Different temperature scales. Thermometer with

Kelvin scale.

gas laws, kinetic theory of gases

Gas state of the matter

1.)The atoms or molecules of the

gas move randomly with high speed

occuping the whole of the space

in which they are contained.

2.) Weak Van der waal’s forces are

acting between the particles.

3.) The density and viscosity of gases

much lower than solids and fluids.

4.) Distance between the particles

is large compared with their diameter.

They can be highly compressed!

Ideal gas

1.) The particles of the gases

move randomly.

2.) They collide with each other

and the wall of the container

completely ellastically (there is no

momentum and energy loss during

the collision).

3.) The intermolecular forces are

negligible.

4. Most of the gases under standard

condition behave as an ideal gas

(almost).

• The thermodynamics describes how the heat influences the state of the matter by defining the state variables such as volume (V), pressure (p), temperature (T), internal energy (U) etc.

• Gas laws give the relationship between the state variables when the matter is in the gas state.

• Kinetic theory of the gases describes the macroscopic properties of the system from microscopic point of view.

Thermodynamics

Heat Motion

GAS LOWS I. (EQUATION OF STATE) IZOTHERMAL PROCESS

1 1 2 2

constant

Boyle's law

constant

1constant

1( : )

T

pV

pV p V

pV

hyperbola yx

1. example

• We have a cylinder filled with gas with the volume of 1 m3 and the pressure of the gas is the normal atmospheric pressure.

What will be the pressure of the gas after pushing in the piston into the cylinder and so reducing the volume to 0,3 m3?

(The temperature does not change.)

GAS LOW II. ISOBARIC PROCESS

1 2

1 2

constant

Gay - Lussac's I. law

constant

p

V

T

V V

T T

GAS LOWS III. ISOCHORIC PROCESS

1 2

1 2

constant

Gay - Lussac's II. law

constant

V

p

T

p p

T T

2. example

• We have a container closed with a piston. The container is filled with gas which tempearute is 20°C and it’s volume is 80 cm3.

• What will be the volume of the gas, after heating up it up to 60°C. (the piston can freely move, that is the pressure is constant)

Avogadro’s law Equal volumes of ideal or perfect gases, at the same temperature and

pressure, contain the same number of particles, or molecules.

Amedeo Avogadro

(1776 – 1856)

cn

V

Standard state of gas!

How would you demonstrate Avogadro’s

law?

V: volume of the gas

n: Number of the moles

Combined and ideal gas law

Kmol

JR

3143,8

cVp

cT

V

cT

pGuy-Lussac II.:

Boyle-Marriote:

Guy-Lussac I.: cT

Vp

Tn

VpR

The ideal gas law can be derived from the combined gas law and

Avogadro’s law !

Universal gas constant (R) gives

the amount of energy required to

increase the temperature of

1 mol gas by one Kelvin.

Ideal gas law.

Combined gas law.

TRnVp

TkNVp k=1,381*10-23 J/K

THERMODYNAMIC SYSTEM

System: the material in the portion of space to be analyzed Surroundings: exterior environment Boundary: A separator, real or imaginary, between system and surroundings

System

Surroundings

Boundary

TERMODYNAMIC SYSTEM Exchanges of work, heat, or matter between the system and the surroundings take place across this boundary.

Mass Energy

Mass

Energy

Mass (-)

Energy (-)

System

Thermodynamics systems

Open

Closed

Isolated

Mass and energy exchange!

Only energy exchange!

Neither mass nor energy exchange!

The thermodynamic state of a system is defined by specifying a set of measurable properties sufficient so that all remaining properties are determined.

THE PROPERTIES OF THE THERMODYNAMIC SYSTEM

macroscopic variables: pressure (p) – momentum transferred to walls by molecular impacts temperature (T) – molecular speeds (gas) or amplitudes of atomic vibrations (solids) volume (V)

UNITS OF THERMODYNAMIC PROPERTIES (SI, OR METRIC)

• pressure: Pascal = Pa = N/m2; = 10-5 atm

• temperature: Kelvins (K) or degrees – Celsius: oC = K – 273 (strictly, not SI)

• volume: cubic meters (m3)

18

EXTENSIVE AND INTENSIVE QUANTITIES

The macroscopic quantities only have a well defiend values that can be determined at each certain state of the thermodynamic system (however the system is composed of sufficient number of microparticles).

Dividing the system into sub-system can be distinguished.. • Extensive quantities : value proportional to amount in

system: m, V, E, Q (electric charge), N (particle count)

• Intensive quantities: value independent of the amount of material: p, T

Expansion work

HEAT: Q (Joule) • Energy transfer between the thermodynamic system and the

enviroment,

followed by heat production or phase transition

• Heat exchange:

- conduction: the heat flows through the particles of the body itself, through molecular vibration.

- convection: heat is transferred through the flow of a liquid or a gas.

- radiation: heat is transferred without heating the medium

• Heat is not a property of a system, but instead is always associated with a process

Phase transitions of matter

Melting Evaporation

Freezing Condensation

Solid Fluid Gas

Solid: the position of atoms and molecules are fixed, only vibrational motion, low degree of freedom, highly ordered state of the matter.

Fluid: the position of atoms and molecules are not fixed, translational, rotational, vibrational motion, higher degree of freedom. Gas: the position of atoms and molecules are not fixed, highest degree of freedom, most disordered state of matter.

How can we calculate the amount of heat taken up by a system? (Heat capacity,

specific heat) Heat capacity (C): is the measure of heat energy required to increase the temperature of a system by 1 kelvin. Unit: J/K Specific heat (c): is the measure of heat energy required to increase the temperature of 1 kg system by 1 Kelvin. Unit: J/kg*K

The specific heat measured under isobar conditions (cp) is always higher than the specific heat under isometric conditions (cv)!

vp cc

Latent heat

Latent heat: the amount of heat which is absorbed (or realesed from) by the system during the phase transion.

Specific latent heat (L): the amount of heat which is absorbed (or realesed) by 1kg of system during the phase transion.

TCQ

K

JC

T

QC

With temperature chamge

Heat capacity

LmQ

kg

JL

m

QL ][

Without temperature change

Latent heat

Phase diagramm of water

Water at its triple point

(0,01 oC, 0,006 atm).

3. example 2 kg ice (0 o C) melts after placing it in to 10 l

water (20 o C) . The specific latent heat of the melting is 334 KJ/Kg. What is the temperature of the water after the melting if the specific heat of the water is 4,2 KJ/Kg* K (density 1000kg/m3) ?

INTERNAL ENERGY

U: Joules (J or kJ), calorie or kcal also use

1 cal = 4.184 J 1 kcal = 4.184 kJ

In thermodynamics, the internal energy (U) is the total energy contained by a thermodynamic system.

U= Eel+Evibr+Erot+Ekin+Eother

The internal energy is a state function of a system

It is an extensive quantity

THE INTERNAL ENERGY IS A STATE FUNCTION

• State function: its value depends only on the current state of the system and not on the path taken or process undergone to arrive at this state.

• Other state functions: enthalpy (H), free energy (F), free enthalpy (G), entropy (S)

LAWS OF THERMODYNAMICS

0. LAW OF THERMODYNAMICS

• If two systems (A and B) are independently in equilibrium with a third one (C), then they are in equilibrium with each other as well.

• Between different points of a system in equilibrium, the intensive variables are equal (there are no thermodynamic currents).

∆U = Q + W

W = − p∆V

• Law of conservation of energy.

• Energy may be converted into different forms, but the total energy of the system remains constant.

• The change in the internal energy of the system is the sum of the supplied heat (Q) and the work (W) done on the system.

I. LAWS OF THERMODYNAMICS:

APPLICATIONS OF I. LAWS OF THERMODYNAMICS

1.) The gas expands, so it does work

on the surroundings (volumetric work)

How does the internal energy of an ideal gas change in an isobaric process

VpW

WQU

2.) The temperature of the gas

increases, so the internal energy of

that increases as well

Q

W

TmcU p

Thermal efficiency: the ratio

of the work done by the

system and the heat taken

up by the sytem.

0W

QU

1.) There is no change in the volume of

the gas, so there is no volumetric work.

2.) The heat energy increases the

internal energy

TcmQ v

How does the internal energy of an ideal gas change in an isochor process

How does the internal energy of an ideal gas change in an isotherm process

0 WQU

2

1

p

plnTRW

1.) The gas expands, so it does

volumetric work on the surroundings.

Temperature remains constant, so

the internal energy doesn’t change!

1.) Heat energy is not given to the

gas.

2.) The expansion of the gas

decreases of the internal energy

of the gas.

0Q

How does the internal energy of an ideal

gas change in an adiabatic process

WU

• Microstate: microscopic parameters of all the particles of the system (e.g. position, velocity),

• Macrostate: distribution of macroscopic parameters (e.g.temperature, pressure, density, energy)

• The number of microstates that belong to the same macrostate is called thermodynamic probability:Ω

WHAT ARE THE POTENTIAL FUNCTIONS? (= STATE FUNCTIONS)

• Internal energy (U)

• Entropy (S)

• Enthalpy (H)

• Free energy (F)

• Gibbs free energy (G)

State: The sum of the thermodynamic quantities of the system.

Quantities: measurable values, which can characterize the state of the system, extensive, intensive ( e.g. p, V, T)

pV = nRT (equation of state)

State functions = potential function: is determined by the initial and the final states of the system, no matter how the system completed the process, which states is passed through

ENTHALPY H (J) I. Law of TD: ΔU = Q + Wall = Q + Weffective – Wexpansion

Wexpansion = -pΔV

ΔU + pΔV = Q + Weffective

ΔU + pΔV = ΔH H = U + pV

✔ measure of the total energy ✔ It includes the internal energy and the amount of energy required to make room for the system if the pressure of the environment remained constant ✔ Potential function ✔ Extensive quantity ✔ The total amount of it can not be measured, only the change of it ✔ For quasistatic processes under constant pressure, ΔH is equal to the change in the internal energy of the system, plus the work that the system has done on its surroundings.

P = const

V ≠ const

H = U + pV H

U pV ✔ Extensive quantity ✔ State function (potential function)

Processes proceeding at constant volume:

V = const. ΔU = Q W=0

heat increases the internal energy

Processes proceeding at constant pressure:

p = const ΔU = Q – pΔV ΔU < Q

ΔU + PΔV = Q = ΔH

heat increases the enthalpy

✔ In basic chemistry scientists are typically interested in experiments conducted a atmospheric pressure and for reaction energy calculations they care about the total energy in such conditions, and therefore typically need to use H. ✔ The increase in enthalpy of a system is exactly equal to the energy added through heat, provided that the system is under constant pressure and that the only work done on the system is expansion work:

Wexpansion = -pΔV

✔ Expansion work is the transfer of energy between the system and its environment through changes in the system's volume, it is non-mechanical work!!

FREE ENERGY , F

I. Law of TD: ΔU = Q + W

II. Law of TD: Q ≤ TΔS

ΔU ≤ TΔS + W

ΔU – TΔS ≤ W

ΔF = ΔU – TΔS ≤ W F = U - TS

U = F + TS

Free energy: out of the total energy this amount can be use for effective work Bound energy: cannot be

used for effective work, it stays in the system as heat

F = F (V,T)

Helmholtz free energy

✔ Free energy = “Useful” work obtainable from a closed thermodynamic system at a constant temperature and volume. ✔ For such a system, the negative of the difference in the Helmholtz energy is equal to the maximum amount of work extractable from a thermodynamic process in which temperature and volume are held constant. ✔ Under these conditions (T = const, V = const), free energy is minimized at equilibrium.

FREE ENTHAPLY , G (Gibbs free energy)

G = H –TS

G = U + pV - TS H = G + TS

Gibbs free energy Bound energy

G = G

(p,T)

✔ Gibbs free energy = “Useful” work obtainable from a closed thermodynamic system at a constant temperature and pressure. ✔ Gibbs energy (also referred to as ∆G) is also the chemical potential that is minimized when a system reaches equilibrium at constant pressure and temperature.

✔ The change in Gibbs free energy associated with a chemical reaction is a useful indicator of whether the reaction will proceed spontaneously. Since the change in free energy is equal to the maximum useful work which can be accomplished by the reaction

ΔG = Wmax

✔ then a negative ΔG associated with a reaction indicates that it can happen spontaneously.

CONNECTION BETWEEN POTENTIAL FUNCTIONS

H

U pV

pV F TS

TS G

Homework

What happen after mixing of 10l,30 o C water and

1,5 kg mass of ice (0 o C)?What is the common

temparature if the specific heat of the water is 4,2 KJ/Kg* K (density1000kg/m3) ?