1

Lecture 5-6

Basic Thermodynamics.The First Law.

References.• Chemistry3 , Chapter 14, Energy and

Thermochemistry, pp.658-700.• Elements of Physical Chemistry, 5th edition,

Atkins & de Paula, Chapter 2, Thermodynamics: the first law.pp. 41-62.

• Physical Chemistry 8th Edition Atkins & de Physical Chemistry, 8 Edition, Atkins & de Paula, The First Law, Chapter 2, pp.28-75.

• Chemistry and Chemical Reactivity, Kotz, Treichel, Townsend, 7th edition, Chapter 5, pp.208-253.

Typical energy estimates

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Thermodynamics : some general comments

Thermodynamics is concerned with energy transformations in chemical and physical systems.Thermodynamics is an experimental science based on a small number ofprinciples that are generalizations made from experience.Thermodynamics is concerned with the macroscopic or large scaleproperties of matter and makes no hypothesis about the small scale or

http://en.wikipedia.org/wiki/Thermodynamics

microscopic structure of matter. The latter is the domain of Statistical Thermodynamics.Chemical Thermodynamics deals specifically with chemical systems andprovides criteria for determining whether or not a particular chemical reaction will proceed, and if it does, to what extent.

Basic Definitions

Energetic transformations take place within regions of space. A specifiedcollection of material particles enclosed in a specified real or hypotheticalboundary is said to constitute a thermodynamic system.The surroundings or environment is labelled as any region outside the system.W d m s in in th s ndin sWe do our measuring in the surroundings.The system and surroundings are separated by a boundary.In an isolated system there is no transfer of either energy or matterbetween the system and the surroundings.In a closed system there is transfer of energy but not of matter acrossthe system/environment boundary.In an open system both energy and matter can be transferred betweenthe system and the surroundings.

• SYSTEM– The object under j

study• SURROUNDINGS

– Everything outside the system

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Work, Heat and energy

Energy: Energy is defined as the capacity to do work . Work and heat are two fundamental waysBy which energy may be transferred to or from a system, and so the energy of a system can be changed by work and heat. Units: joules (J) or kJ mol-1.Work: Work is a form of energy which can transfer in and out of a system, that is stored inthe organized motion of molecules. Work is done when an object is moved against some opposingforce.Heat: Heat is a form of energy which can transfer in and out of a system that is stored in therandom motion (thermal motion) of molecules If an energy difference of a system results from

Kotz, section 5.1, pp.209-214.Chemistry3, section 14.1, pp.660-666.

random motion (thermal motion) of molecules. If an energy difference of a system results froma temperature difference between it and the surroundings, energy has been transferred as heat.

Thermodynamic definitions of work and heat.

The system may be thought of as an energy bank. Transactions with the bank can be made in two kinds of currency – work and heat. Once the currencies are inside the bank they are stored simply as energy reserves and may be withdrawn in any currency.

Thermodynamically speaking heat and work are not forms of energy but areprocesses by which the total energy (the internal energy) of a system is h dchanged.

The quantity of energy transferred as work during a transaction with the system is denoted as W (units: J or kJ). Work done on the system is regarded as positive since the latter work results in anincrease in the energy of the system. In contrast the work done by the system is negative due to the fact that the system loses energy by doing work on the surroundings.

The total energy of a system at any given time is termed the internal energyU (or E). It comes from the total kinetic and potential energy of the molecules which compose the system.

Heat q (units: J or kJ) is energy which is transferred across the boundary of a thermodynamic system during a change in its state by virtue of a difference in temperature between the system and its surroundings.When heat is transferred to the system, q is positive, since the heat transfer process results in an increase in the internal energy of the system. If heat energy is transferred from the system, q is negative, because the internal energy decreases.

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Energy transfer as heat occurs spontaneously from an object at a higher temperatureto an object at a lower temperature.

Transfer of energy as heat continues until both objects are at the same temperature,and thermal equilibrium is achieved.

Directionality and extent of heat transfer.

After thermal equilibrium is attained the object whose temperature has increased has gained thermal energy and the object whose temperature has decreased has lostthermal energy.

Directionality of heat transfer is described as exothermic or endothermic.In an exothermic process thermal energy is transferred from a system to its surroundings.The energy of the system decreases and the energy of the surroundings increases.In an endothermic process thermal energy is transferred from the surroundings to the system, increasing the energy of the system and decreasing the energy of the surroundings.

Directionality of Energy TransferDirectionality of Energy Transfer• Energy transfer as heat is always from a

hotter object to a cooler one.

• EXOthermic: energy transfers from • EXOthermic: energy transfers from SYSTEM to SURROUNDINGS.

T(system) goes downT(system) goes downT(surr) goes upT(surr) goes up

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Directionality of Energy TransferDirectionality of Energy Transfer• Energy transfer at heat is always from a

hotter object to a cooler one.

ENDOth i h t t f f • ENDOthermic: heat transfers from SURROUNDINGS to the SYSTEM.

T(system) goes upT(system) goes upT (surr) goes downT (surr) goes down

Heat is the transfer of energy thatcauses or utilizes random or chaotic motion in the surroundings.Heat is energy which is transferredacross the boundary of a thermodynamic system during a change in its state byvirtue of a difference in temperature Between the system and its surroundings.

Work is the transfer of energy thatcauses or utilizes uniform motion of atoms in the surroundings.Work is energy which is transferred acrossThe boundary of a thermodynamic systemDuring a change in its state and which canBr converted completely into the ‘lifting of a weight’ in the surroundings (i.e., motion ofA mass against opposing force).

Thermodynamic sign convention:q and w are positive if energy enters the system(as work and heat respectively), but negative ifEnergy leaves the system.

6

)(2 22 gHZnClHClZn +→+

7

First Law of Thermodynamics: Internal energy U or E.Internal energy (U or E) : is the total energy of the system at any given time. Comes from the total kinetic and potential energy of molecules which compose the system.Change in internal energy (ΔU or ΔE) : energy change as system goes from an initial state withenergy Ui to a final state with energy Uf. Hence ΔU = Uf – Ui.We suppose that a closed system undergoes a process by which it passes from a state A to a state B. Then the change in internal energy ΔU = UB – UA is given by ΔU = q +W.The first law may be cast in differential form corresponding to the situation here there isan infinitesimal change in internal energy dU caused by the addition of an infinitesimal quantityof heat d’q and the performance of an infinitesimal amount of work d’w on the system. HenceWe can write: dU d’q + d’w We note that d’q and d’w are inexact differentials they cannot be We can write: dU = d q + d w. We note that d q and d w are inexact differentials – they cannot be evaluated from a knowledge of the initial and final states alone.

System

q+ W+UΔ+

Heat transfer to system

Kotz, section 5.4. pp.222-224

Surroundings U q WΔ = +

Increase in internalenergy

Work done on systemWe area led therefore to the importantconclusion that the energy of an isolatedsystem is constant.In an isolated system there is no transferof heat or work and so q = 0 and W = 0.Hence ΔU = 0 hence U = constant.

This is a mathematical statement of theFirst Law of Thermodynamics.

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InitialState

gy U

UIFinal State

y U

UF

Law of conservation of energy : Total energy of the Universe is constant,

0=Δ+Δ=Δ gssurroundinsystemuniverse UUU

Finalstate

Inte

rnal

Ene

rg

UF

0<−=Δ<

IF

IF

UUUUU

Initialstate

Inte

rnal

Ene

rgy

UI

0>−=Δ>

IF

IF

UUUUU

Energy lostto surroundingsEnergy gained

from surroundings

Endoergic energy transferfrom surroundings to system.

0sysq >Endothermic (refers to energy transfer as heat).

Exoergic energy transferFrom system to surroundings.

Exothermic (refers to energy transfer as heat)

0sysq <

9

Change Sign convention Effect on Usystem

Thermal energy transfer to system(Endothermic)

q > 0 (+ve) U increases

Thermal energy transfer from system(Exothermic)

q < 0 (-ve) U decreases

Energy transfer as k d

W > 0 (+ve) U increaseswork done on systemEnergy transfer as work done by system

W < 0 (-ve) U decreases

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Work done in isothermal (constant temperature) expansion of a gas.

We calculate the work done when a system expandsfrom an initial volume Vi to a final volume Vf, a changegiven by ΔV = Vf-Vi.Consider a piston of area A moving out through a distance h. The piston represents the movingboundary between the expanding gas and thesurrounding atmosphere.Th f i th i i th t tThe force opposing the expansion is the constantexternal pressure Pext multiplied by the piston area A.Hence F = PextA.The work done is w = F h = PextA h = PextΔV.Note that hA is the volume of the cylinder sweptout by the piston as the gas expands.We must also consider the sign of the work.Since the system does work on the surroundingsit loses energy and the work done is negative. Since ΔVis positive we need to introduce a negative sign into thework expression to ensure that w is negative when See AdP, Elements PChem 5,

p 46 for a full discussion ofp gΔV is positive. If the system is in mechanicalEquilibrium with the surroundings at every stage of the expansion,Then we have a reversible expansion, the maximumExpansion work is done and Pext = P, the gas pressure.

VPw Δ−=

p.46 for a full discussion ofReversible expansion.

Reversible isothermal expansion of ideal gas.

Total work done w is given by

∫∫ −=′= f

i

V

VPdVwdw

Indicator diagram : reversible isothermalexpansion of ideal gas from initial statedefined by (Pi,Vi) to final state defined by (Pf,Vf).Work done given by shaded area under curve.

Fluid is ideal gas hence

VnRTP =

Work done:

[ ]⎭⎬⎫

⎩⎨⎧

−=−=−= ∫ fVV

V

V VV

nRTVnRTVdVnRTw f

i

f lnln⎭⎩

∫i

V VVi

In an expansion Vf > Vi so Vf/Vi > 1, and ln(Vf/Vi ) is positive, and w is negative since energy leaves the system as the system does expansion work.

For a given change of volume and fixed amount of gas, thework done is greater the higher the temperature.

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In general the work done on a system is expressed as the product of a generalisedForce X and a generalised displacement dξ, hence w = X.dξ.

Work type d’w comment units

‘PV’ work P dV P = pressure P Nm-2PV work - P dV P = pressuredV = volume

change

P, Nm-2

V, m3

Surface area change

γ dA γ = surface tension

dA = area change

γ, Nm-1

A, m2

Length change f dL f = tensiondL = length

change

f, NL, m

Electrical work E dQ E= electric E,VElectrical work E dQ E electric potential

Q = electric charge

E,VQ, C

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HEAT CAPACITYHEAT CAPACITY

The heat required to raise an

Kotz, section 5.2. pp.215-218.

The heat required to raise an object’s Temperature by 1 ˚C.

Which has the larger heat capacity?Which has the larger heat capacity?

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Heat Capacity

Increasing temperature increases the internal energy of a system. The exact increase depends upon the heating conditions.Heat cannot be detected or measured directly. There is no ‘heat meter’.One way to determine the magnitude of a heat transfer is to measure the work needed to bring b t th h i th th d i t t

Can also define specific heat capacity c according to c = C/m where m = mass of substance with unitsJ K-1g-1 or the molar heat capacity Cm as Cm = C/n with units: J K-1mol-1.The heat capacity depends on whether a sample is maintained at constant volume (C = CV) or constant pressure (C = CP) The respective about the same change in the thermodynamic state

of a system as was produced by heat transfer. Another approach is to deduce the magnitude of a heat transfer from its effects: namely, a temperature change. When a substance is heated the temperature typically rises. For a specified energy q transferred by heating, the magnitude of the resulting temperature change ΔT depends on the heat capacity C of the substance.We can therefore simply measure the heat absorbed or released by a system :

constant pressure (C = CP). The respective molar quantities are CV,m and CP,m.

y yWe determine the temperature change and use the appropriate value of the heat capacity of the system.Units of C are J K-1.Heat capacity is an extensive property.

TqCΔ

= TCq Δ=

Loss of energy into the surroundings can bedetected by noting whether the temperaturechanges as the process proceeds.This is the principle of a calorimeter.

The bomb calorimeter

From the first law of thermodynamics we recall

VPqU Δ−=Δ

If the reaction is performed in a closed container called a bomb calorimeterthen the volume remainsconstant and ΔV = 0.Hence the first law reduces to

VqU =Δ

Hence to measure a change in internal energy we should use a fixed volume calorimeter and monitor the energy released (q < 0)

Combustion reaction

No heat flow

monitor the energy released (q 0) or supplied (q > 0) as heat by measuring the corresponding change in temperature.

VTV

VV

TU

dTdU

TULimC

TU

TqC

⎟⎠⎞

⎜⎝⎛∂∂

==ΔΔ

=

ΔΔ

=Δ

=

→Δ 0Chemistry3, Ch.14. pp.693-698

Kotz, section 5.6. pp.229-233.

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Calorimetry defines the study of heat transfer during physical and chemical processes.A calorimeter is a device for measuring energy transferred as heat.In an adiabatic bomb calorimeter the process which we wish to study (a chemical reaction) is initiated inside a constant volume container (the bomb). The latter is immersed inside a stirred

Calorimetry : some details.

( )water bath. The whole arrangement (container + water bath) defines the calorimeter. The calorimeter is also immersed in an outer waterbath. The water in the calorimeter and in the outer water bath ismonitored and adjusted to the same temperature. This arrangementensures there is no net loss of heat from the calorimeter to thesurroundings (the bath). Hence the calorimeter is adiabatic.The change in temperature ΔT of the calorimeter is proportionalto the heat that the reaction releases or absorbs. Hence by measuring ΔT we can determine qV and hence find ΔU.

We calibrate the calorimeter using a process of known energy outputWe calibrate the calorimeter using a process of known energy outputand determining the calorimeter constant C in the relation q = CΔT.The calorimeter constant may be measured electrically by passinga constant current I from a source of known potential difference Vthrough a heater for a given period of time t and noting that q = VIt. Alternatively C may be determined by burning a known mass of substance (benzoic acid is often used) that has a known heat output. With C determined is is simple to interpret an observed temperature rise as a release of heat.

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CalorimetryCalorimetrySome heat from reaction warms waterqwater = (sp. ht.)(water mass)(∆T)qwater p

Some heat from reaction warms “bomb”qbomb = (heat capacity, J/K)(∆T)

Total heat evolved = qtotal = qwater + qbomb

Calculate energy of combustionCalculate energy of combustion (∆U) (∆U) of of

Measuring Heats of ReactionMeasuring Heats of ReactionCALORIMETRYCALORIMETRY

Measuring Heats of ReactionMeasuring Heats of ReactionCALORIMETRYCALORIMETRY

octane. octane. CC88HH1818 + 25/2 O+ 25/2 O22 ff 8 CO8 CO22 + 9 H+ 9 H22OO

•• Burn 1.00 g of octaneBurn 1.00 g of octane•• Temp rises from 25.00 to 33.20 Temp rises from 25.00 to 33.20 ooCC•• Calorimeter contains 1200 g waterCalorimeter contains 1200 g water•• Calorimeter contains 1200. g waterCalorimeter contains 1200. g water•• Heat capacity of bomb = 837 J/KHeat capacity of bomb = 837 J/K

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Step 1Step 1 Calc. energy transferred from reaction to water.Calc. energy transferred from reaction to water.q = (4.184 J/g•K)(1200 g)(8.20 K) = 41,170 Jq = (4.184 J/g•K)(1200 g)(8.20 K) = 41,170 J

Measuring Heats of ReactionMeasuring Heats of ReactionCALORIMETRYCALORIMETRY

Measuring Heats of ReactionMeasuring Heats of ReactionCALORIMETRYCALORIMETRY

q ( g )( g)( ) ,q ( g )( g)( ) ,Step 2Step 2 Calc. energy transferred from reaction to bomb.Calc. energy transferred from reaction to bomb.q = (bomb heat capacity)(∆T)q = (bomb heat capacity)(∆T)

= (837 J/K)(8.20 K) = 6860 J= (837 J/K)(8.20 K) = 6860 JStep 3Step 3 Total energy evolvedTotal energy evolved

41,200 J + 6860 J = 48,060 J41,200 J + 6860 J = 48,060 JEnergy of combustion (∆U) of 1.00 g of octane Energy of combustion (∆U) of 1.00 g of octane

= = -- 48.1 kJ48.1 kJ

Enthalpy

The change in internal energy is not equal to the energy transferred as heat when the system Is free to change its volume. Under such circumstances some of the energy supplied as heat to the system is returned to the surroundings as expansion work.Hence dU < d’q.

We shall show that under constant pressure conditions, theenergy supplied as heat is equal to the change in another

Kotz, pp.225-229.

energy supplied as heat is equal to the change in anotherthermodynamic property of the system, called the enthalpy.

From the first law of thermodynamics for a finite change at constant pressure

VPqU P Δ−=Δ

Now IFIF VVVUUU −=Δ−=Δ

Hence

( )( ) ( ) HHHPVUPVUq

PVPVqVVPqUU

IFIIFFP

IFPIFPIF

Δ=−=+−+=+−=−−=−

Here we have introduced the enthalpy function H as

PVUH +=Hence the heat absorbed at constant pressure equalsthe increase in enthalpy of the system.

HqP Δ=

For an exothermic reaction ΔU < 0, ΔH < 0,whereas for an endothermic reaction, ΔU > 0and ΔH > 0.

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Relationship between ΔU and ΔH.

The enthalpy is given by

PVUH +=For a finite change at constant pressure

( ) ( )PVUPVUH Δ+Δ=+Δ=Δ

The term ΔV is significant for gases.

Assume ideal gas behaviour. At constantT and P we have

nRTPV =For reactants and products

RTnPVRTnPV RxRx

==

( ) ( )

VPUPVVPU

PVUPVUH

Δ+Δ=Δ+Δ+Δ=

Δ+Δ+ΔΔ

Since VP qUqH =Δ=Δ we note that

VPqq VP Δ+=

Hence the heat absorbed at constant pressure

RTnPV PrPr =Hence

( ) ( ) nRTRTnnVVP RxRx Δ=−=− PrPr

whereRxnnn −=Δ Pr

Hence for gas phase species

ΔP=0Constant P

Exceeds that absorbed at constant volume by theAmount PΔV.For condensed phases (liquids, solids) ΔV= Vproducts-VreactantsWill be very small and so ΔV ~0. Hence

UH Δ≅ΔCondensedphases

nRTUH Δ+Δ=Δ

0

PP

V TP

q HCT T

H dH HC LimT dT TΔ →

Δ= =Δ Δ

Δ ∂⎛ ⎞= = = ⎜ ⎟Δ ∂⎝ ⎠Temperature variationof enthalpy.