physical chem

thermodynamics

the study of energy transformations and their reaction to macroscopic variables such as temperature, pressure and volume

applicable to all processes involving temperature and pressure

systems and surroundings

system is the part of the universe being studied

surroundings are everything outside the system

the boundary seperates the system from surroundings

types of systems

open system- exchanges mass and energy

closed system- exchanges energy only

isolated system- exchanges neither

ex. isolated system- thermos flask preventing heat flow

types of thermodynamic processes

isothermal- constant variable is temperature, ex. is water bath

isobaric- constant variable is pressure, ex. is cooking in an open pan

isochoric- constant variable is volume, ex. is pressure cooker

internal energy

internal energy of a system changes when heat or work is transferred

relationship-

delta V= delta W + delta Q

Q- heat added or removed

V- change in internal energy

W- work added or removed

heat- energy used to increase temperature, heat is not the same as temperature

work- energy used to move matter, ex. expanding gas performs work, compressing gas performs work

thermodynamic equilibrium

a system reaches this when it no longer changes with time, ex. 2 objects at different temperatures exchange heat until they reach the same final temperature

intensive vs extensive variables

intensive variables- do not depend on system sie

ex. temperature T, pressure P, mole fraction x

extensive variables- depend on system size

ex. volume V, number of moles n, internal energy U

state variables

properties that depend only on the thermodynamic state, not the path taken

ex. P, T, V, n, U

non state variables

depends on the process/path

ex. Heat Q, work W

straight line distance between wageninigen and amsterdam= state variable

driving distance depends on route= non state variable

0th law of thermodynamics

if 2 bodies are separately in thermal equilibrium with a third body they are in thermal equilibrium with each other

defines the concept of temperature

temperature scales

celsius scales- water boils at 100 degrees at 1 atm

kelvin scale- used in science, add 273.15 to celsius

temperatures in thermodynamics should generally be expressed in kelvin

0th law- thermal equilibrium principle, 1st law- energy is conserved, 2nd law- heat flows naturally from hot to cold bodies, 3rd law- absolute zero (0K) can never be reached

Ideal gas law

PV=nRT

P=pressure

V=volume

n=moles

T=temperature in kelvin

R= 8.314 J/K/mol

assumptions- valid only when particles are very small, no intermolecular forces exist, molar volume; v=V/n

why thermodynamics matter in food tech

how to create foods with desired properties, these properties depend on:

-ingredients used, ingredient concentration, processing conditions

-temperature and pressure strongly affect food structure and behaviour

-flavour partitioning; flavour molecules distribute differently between oil and water phases, thermodynamics predicts this partition equilibrium

-phase seperation in biopolymer mixtures- protein polysaccharide mixtures may seperate into 2 phases; one protein rich and one polysaccharide rich which creates unattractive layers in drinks

lever rule

calculate the amount of each phase in a 2 phase system

mole fraction- Xa=Na/N total

lever rule relation- Nb/Nc= Xa,1-Xc,1/Xa,1-Xb,1

used for partially miscible liquids and phase seperated mixtures

Phase diagrams

shows which state of matter exists at different temperatures and pressures

solid- strong interactions and long range order

liquid- weak interaction and short range order

gas- almost no order and very weak interactions

in a phase diagram each region represents one stable phase, the lines between regions are called coexistence curves or phase boundaries and on these boundaries two phases coexist in equilibrium

important curves in the water phase diagram

boiling curve- seperates liquid water and water vapour, at 1 atm water boils at 100 degrees celsius

during boiling temperatures stays constant as all added heat is used for the phase transition → this heat is called latent heat

pressure affects boiling

higher pressure → higher boiling point (pressure cooking)

lower pressure → lower boiling point (vacuum cooking)

at high altitude potatoes cook more slowly because water boils at a lower temperature (high altitude = low pressure)

melting curve

seperates solid and liquid phases-

melting; solid → liquid

freezing; liquid → solid

also requires latent heat

water is unusual because ice expands when freezing, the melting curve has a negative slope, increasing pressure can melt ice which explains ice skating (thin water layer forms under skates due to pressure)

sublimation curve

seperates solid and gas phases

sublimation = solid → gas

deposition = gas → solid

freeze drying- a practical application;

1) water in food is frozen

2) pressure is lowered

3) ice sublimates directly into vapor

used for instant coffee, long shelf life foods, outdoor foods

triple point and critical point

triple point- the point where solid, liquid, and gas coexist

for water- 273.16K, 0.006 atm

used for thermometer calibration

critical point- for water 647.15K, 218 atm, above this point no clear distinction exists between liquid and gas, the substance becomes a supercritical fluid

you can move from liquid to gas in 2 ways; cross the boiling curve and phase transition occurs or go around the critical point and gradual change with no phase transition occurs

applications in food technology

liquid nitrogen boils at 77K, used for rapid freezing because it is extremely cold and chemically inert, applications are removing oxygen from wine bottles and drinks before sealing, increasing pressure inside cans to strengthen them

guiness widget- a plastic ball with a tiny hole added to guines cans, LN2 pressurizes both the can and the widget, when opened the widget releases gas rapidly which produces smooth foam

carbon dioxide and dry ice- CO2 triple point at 5atm and 216K, at atmospheric pressure solid CO2 cannot melt; it sublimates directly into gas, this solid CO2 is called dry ice; temperature is 194K, useful for refridgerated transport and packaging

heating processes

isochoric heating (constant volume)

ex. pressure cooker

because volume is fixed; heating increases pressure, liquid and vapour coexist, the system follows the boiling curve

important values-

20 degrees celsius- vapour pressure is 0.023 atm

70 degrees- 0.5 atm

100 degrees- 1 atm

121 degrees- 2 atm (safety valve opens)

why pressure rises- more molecules enter gas phase, gas pressure increases, harder for liquid molecules to evaporate, boiling point increases, this explains why pressure cookers cook faster

isobaric heating (constant pressure)

ex. container with movable lid at 1atm

process-

heat liquid water from 20 degrees celsius, temperature rises until boiling point (100 degrees), at boiling point liquid turns to vapour and temperature and pressure remain constant and volume increases because gas is less dense, after all liquid evaporates further heating increases temperature and volume

phase diagrams of other substances

water behaves differently from most substances because it expands upon freezing

ex. CO2 melting curve has a normal positive slope, does not behave like water

Phase diagram of salt water (NaCl + water)

food systems are usually mixtures, not pure substances

for salt water- horizontal axis is NaCl concentration, vertical axis is temperature, diagram valid only at atmospheric pressure

cooling salt water-

ex. start with 10% NaCl at 10 degrees celsius, cooling below freezing forms pure ice crystals, remaining liquid becomes more concentrated in salt, further cooling creates more ice and increases salt concentration further, the system follows the melting curve during freezing

lever rule salt system

calculates how much of each phase exists in a 2 phase system

for salt water, phase A is pure ice, and phase B is concentrated salt solution

the relation is

Nb= moles in phase B

Nc= total moles

X= mole fractions of a component

it allows calculation of ice formed, amount and concentration of remaining salt solution

ideal gas law

assumes particles are point like, particles do not interact, works best at low pressure, high temperature, dilute gases

real gases and corrections

real gases deviate from ideal behaviour because particles interact, particles have finite size

virial equation

adds correction terms;

van der waals equation

includes attraction between particles, finite particle size, this model describes real gases better than ideal gas law

conservation of energy

energy cannot be created or destroyed, only transformed from one form into another, the total energy of an isolated system (and the universe) is always constant

fundamental formula- delta U= delta W + delta Q

can all take positive or negative values depending on the direction of energy flow

for an ideal gas, internal energy is strictly a function of temperature

Cv is heat capacity at constant volume, yielding 3 special process paths

1) isothermal process (change of T is zero), internal energy remains constant (change in internal energy is zero) therefore any heat added turns completely into work, change in Q= -change in W

2) isochoric process; constant volume because volume doesn’t change, no expansion or compression work can be done (change in W=0), therefore change in U= change in Q

3) adiabatic process; no heat flow, the system is thermally insulated from its surroundings meaning change in Q=0, so change in U= change in W

adiabatic processes+ adiabatic cooking

while perfect physical insulation doesn’t exist, very fast processes leave no time for heat to exchange across boundaries so rapid expansions/compressions in real life are safely assumed to be adiabatic (change in Q=0)

mechanism adiabatic cooling- when pressure is lowered quickly, a gas expands, to expand the system must perform mechanical work on its surroundings so delta W<0

because no heat can enter to replenish this energy (change Q=0) the energy must come from the gas’s own internal energy reserve, causing change in U to decrease, delta U<0

since delta U=nCvdelta T a drop in internal energy directly forces the temperature of the gas to drop

ex. opening a soda can; carbonated drinks contain compressed CO2 and cracking the tab open causes the gas to expand instantly and undergo adiabatic cooling, sudden localised drop in temperature causes the moisture in the ambient air to condense into a visible cloud/smoke flume

entropy (S)

thermodynamic property that quantifies degree of molecular disorder or randomness within a system

Boltzmann equation-

the lattice game model- a 4×4 vertical lattice grid containing 4 identical particles demonstrates that uniform, spread out configurations possess a significantly higher count of micro states (W) than highly organized configurations, systems naturally progress towards these disordered macro states simply because they are statistically the most probable arrangements

general behaviours

entropy increases during transitions that give molecules more structural freedom; solid → liquid → gas, it decreases during condensation/freezing

2nd law of thermodynamics- the entropy of the universe always strives to increase ( delta S universe >0) , this law dictates that heat flows spontaneously from a hot object to a cold object, never the reverse

entropic elasticity in food polymers; long polymer chains like gelatin networks/proteins naturally exist in highly curled disordered configurations to maximise their entropy, pulling/stretching the polymer forces the chain into a straight, highly ordered configuration which lowers its entropy, when you release the stretching tension, the molecules spontaneously snap back into their curled states to maximise their entropy, creating an elastic pulling force

enthalpy

represents the total heat content of a system and is defined mathematically as -

state vs path functions; unlike heat (Q) and work (W) which are path dependent, enthalpy (H) and internal energy (Q) are state variables, their values depend entirely on the current state of the system, not on how the system reached that state

when a process occurs under constant atmospheric pressure (change in pressure=0) the change in enthalpy is exactly equal to heat exchanged with the surroundings

molar latent heats- phase transitions involve shifts in enpalthy without changing temperature, quantified as;

molar heat of fusion/melting (delta H fus)

molar heat of vaporisation (delta H vap)

molar heat of sublimation (delta H sub)

Gibbs free energy (G)

the thermodynamic potential used to determine if a process can happen spontaneously at constant temperature (T) and pressure (P)

temperature driven spontaneity examples-

ice melting- breaking hydrogen bonds of ice requires heat (change H>0) but liquid water is more disordered than ice (change S>0) at low temperature, the change H term dominates ( change G>0, ice stays frozen) at high temp, above 0 degrees the -TchangeS term outbalances change H causing change G<0 making melting spontaneous

boiling an egg- unfolding compact egg proteins requires input heat to break structural bonds (change H>0) but denaturing them into open random coils increases disorder (change S>0), at boiling temperatures the magnitude of the -TchangeS term becomes larger than change H forcing change G<0 this allows the proteins to spontaneously denature and form a solid gel

chemical potential (u)

gibbs free energy per mole of a specific substance

systems naturally minimise their gibbs free energy, matter always moves spontaneously from a region of high chemical potential to a region of low chemical potential, at thermodynamic equilibrium the chemical potential of a substance must be equal everywhere in the system

phase stability- the most stable state of matter under any given temperature/pressure is always the phase that possess the absolute lowest chemical potential (u)

along a phase boundary line, the potentials of 2 phases are equal ( ex. on the boiling line; u liquid= u gas), at the triple point all 3 phases coexist in balance ( u solid= u liquid= u gas)

temperature dependence

The rate of change of chemical potential with temperature is proportional to negative molar entropy (s)

because molar entropy increases across states of aggregation (S solid < S liquid < S gas) lines plotted on a u vs. T graph slope downward, the gas phase has the steepest downward slopes, explaining why it becomes stable u phase at high temperatures

pressure dependence

the rate of change of chemical potential with rpessure is equal to the molar volume (v)

increasing pressure increases the chemical potential, exception when water expands when freezing so V ice> V water, increasing pressure raises the chemical potential of ice faster than liquid water explaining why applying pressure lowers the melting point of ice

isothermal compression of an ideal gas

extension to mixtures, in a multi component mixture, gas pressures are replaced by concentrations or mole fractions (xi) defining the chemical potential of components i as;

• μi​ = chemical potential of component i in the mixture.

• μi∗= chemical potential of the pure component i at the same temperature and pressure (the reference state).

entropy of mixing

when 2 components mix the number of possible arrangements (microstates) increases

resulting-

Smixture does not equal S1 + S2

mixing creates additional disorder, therefore entropy increases

ideal mixtures

have no interactions between components, only entropy drives mixing

lattice model visualisation

mole fraction

N1= number of particles of component 1

N= total particles

number of configurations

the number of possible configurations

where-

N= N1+N2

!= factorial

Boltzmann equation

entropy relates to configurations through

S= Kblnw

Kb= boltzmann constant

w= number of microstates

important trend

entropy is maximum at equal at equal mixing

reason- maximum disorder, largest number of configurations

entropy of mixing equation

chemical potential of ideal mixtures

fundamental relation-

u=h-Ts

for ideal mixtures; h=0

because there are no intermolecular interactions

total chemical potential

the mixture contains

1) pure component contributions

2) entropy contribution from mixing

chemical potential of each component

key consequences

As mole fraction decreases;

ln(x) → more negative

and therefore chemical potential decreases

tangent/intercept method

to determine chemical potentials graphically;

1. Plot u/RT vs composition

2. Draw tangent line

3. Use intercepts to find u1, u2

regular mixtures

difference from ideal mixtures, now components interact

example- repulsive interaction between molecules

interaction energy- 1kT

effect of repulsive interactions

particles avoid each other

at low concentration- particles cluster at corners/edges to minimize interaction energy

at higher concentration- clustering becomes stronger

eventually- phase seperation, ex. oil and water

enthalpy of mixing

regular mixtures require an enthalpy term

thermal effects of mixing

ex. ethanol and water

when mixed, temperature increases, therefore X<0, meaning attractive interactions, completely miscible

when does phase seperation occur

critical condition-

X>2

then gibbs free energy develops 2 minima, mixture seperates into 2 phases

gibbs free energy visualisation

physical meaning

system lowers free energy by splitting into

one A rich phase and one B rich phase

binodal region

inside the binodal curve- mixture phase seperates, outside single phase

lever rule

used to calculate the amount of phases

chemical potentials in regular mixtures, full gibbs expression

difference from ideal mixture-

additional enpalthy term

analytical expressions

temperature dependence

the interaction parameter depends on temperature

some mixtures-

mix at high temperatures, seperate at low temperatures

example- h-hexane + nitrobenzene, phase seperation below 293K

phase diagram

example water and nicotine

polymers in solution

polymer configuration depends on entropy and enthalpy

good vs bad solvent

good solvent- interactions; polymer-solvent stronger than polymer-polymer

result- polymer expands

bad solvent- interactions polymer-polymer stronger

result- polymer collapses, compact globule

partition equilibrium

most foods contain- dispersed phases, emulsions, ex. oil in water emulsions, molecules often prefer one phase another

chemical potential in 2 phases

equilibrium condition

partition coefficient

depends on temperature, pressure

food example- mayonnaise contains oil phase, water phase, preservatives distribute between phases according to the partition coefficient, important because fungi grow in water phase, preservative concentration there matters

food application of phase seperation

macroscopic phase seperation often undesirable but microscale phase seperation creates texture ex. cheese, whipped cream, mayo

clausius-claperyon relation

the clasius clapeyron equation describes how pressure changes with temperature along phase coexistence curves

delta s= s1-s2= difference in molar entropy between phases

delta v= v1-v2= difference in molar volume between phases

where delta h is the latent molar heat of the phase transition

application to the boiling curve

for liquid vapour equilibrium- vapor molar volume is much larger than liquid molar volume

therefore-