kuliah KF1 (adiabatik1)

PHYSICAL CHEMISTRYPROSES ADIABATIK

REVERSIBEL

Materi (4x pertemuan)

• Proses adiabatik reversibel• Hukum termodinamika 2

First Law

• dU, U = internal energy change of system

• dq, q = heat transfer into system• dw, w = work done on system

wqU

dwdqdU

Types of Work

• Volume Expansion

w = - Pext dV (P = pressure)• Stretching

w = - dl ( = tension)• Surface Expansion

w = - d ( = surface tension)

• Electricalw = dq ( = electrical potential)

Work

• Work is any interaction that could have as the sole effect the raising of a weight.

• Work = force x distance

dw = F dhw = F dh

• 1 kg

• 1 meter

Work of Expansion/Compression

pex = external pressureA = piston areadh = displacementdV = A dh = volume change for

the gasdw = F dh

Pex = F / A F = Pex A

dw = – Pex (A dh)

dw = – pex dV

gas

dh

pex

A

Reversible Changes

• A reversible change is one that can be reversed by an infinitesimal modification of a variable.

• In a reversible expansion or compression, pex = pgas

pex pgas

Irreversible Changes

• An irreversible change is one that is not reversible.

• In an irreversible expansion, pex < pgas

• In an irreversible compression, pex > pgas

pex pgas

pex pgas

Expansion Work at Constant P

VPdVPw

constP

dVPw

ex

V

V

ex

ex

V

V

ex

2

1

2

1

. le,irreversib if

Isothermal Reversible Work

1

2ln

/ gas, idealan if

,reversible if

2

1

2

1

V

VnRT

V

dVnRTw

VnRTp

pp

dVpw

V

V

gas

gasex

V

V

ex

Indicator Diagram: Compression

0

2

4

6

8

10

0 5 10 15 20

• pex

• Vi• Vf

• additional irreversible work

• reversible

work

Heat

• Heat is the energy transferred across a temperature difference.

• Temperature is the degree of “hotness” of an object.

q

Thigh

Tlow

Heat Capacity (C)

ifT TT

q

dT

qdC lim

0

• The heat capacity of a system is the ratio of the infinitesimal heat transfer dq to the accompanying infinitesimal temperature change dT. C depends on:· temperature· substance· path

Cv: Heat Capacity

2

1

,

,

T

T

mvV

mVV

V

V

TdCnq

TdCnqd

T

dqC

• Note: Heat absorbed at constant volume, qV = ∆U

Cp: Heat Capacity

2

1

,

,

T

T

mpp

mpp

p

p

TdCnq

TdCnqd

T

qC

• Note: Heat absorbed at constant pressure, qp = ∆H

q

Cp and Cv

RnCC

RCC

VP

mVmP

,,

HU PV CC • and • for solids and liquids

Common Paths

• Isochoric: V = constant (dV=0)

• Isobaric: p = constant (dp=0)

• Isothermal: T = constant (dT=0)

• Adiabatic: q = 0

Isothermal vs. Adiabatic

• An adiabatic process in one in which no heat is exchanged between the system and its surroundings.

• An isothermal process in one in which the initial and final temperatures are the same.

• Isothermal processes are not necessarily adiabatic.

Work

• Isochore: w = 0

• Isobar: w = -pV

• Reversible Isotherm: w = -nRT ln(Vf/Vi)

• Adiabat: w = U = nCv,m T

If CV is independent of

temperature between T1 and T2

State vs. Path Function• A state function is a

property of a system that depends only on its current state and not on how that state was reached.

• A path function depends on how the state was reached.

• state A

• state B

• path 1

• path 2

The First Law

• dU = dw + dq defines the internal energy change of a system.

• The internal energy is a function of state.

• Corollary: Energy is conserved in an isolated system.

• state A

• state B• w

• q

• w

• q

Energy Changes

• Because U is a function of state, U depends only on the initial and final states, and not the path followed between them.

if

U

U

UUdUUf

i

Changes in Internal EnergyFor a closed system at constant composition (n), the internal energy (U) of a system is a function of the volume (V) and temperature (T):

U(V, T)

When the volume changes infinitesimally from V to V+dV at constant temperature (T), the internal energy changes from its initial state (Ui) to its final state (Uf):

f i

T

UU U dV

V

Changes in Internal Energy

• If both the temperature and volume change infinitesimal amounts, dT and dV, the internal energy changes from its initial state (Ui) to its final

state (Uf):

f i

T V

U UU U dV dT

V T


• Since the change in internal energy is infinitesimal, we can express the change between the initial and final states as the exact differential dU:

• The significance of this equation is that, in a closed system of constant composition (n), any infinitesimal change in the internal energy (U) is proportional to the infinitesimal changes of volume (V) and temperature (T)

T V

U UdU dV dT

V T


• Recall that the heat capacity at constant volume, CV, is defined as:

• The heat capacity at constant volume, CV, is the slope of the internal energy (U) with respect to the temperature (T) and constant volume (V).

VV

UC

T


• The internal pressure (πT) is the measure of the change in the internal energy of a substance as its volume is changed at constant temperature.

• Mathematically, the internal pressure (πT) is defined as:

TT

U

V


• Because an infinitesimal change in the internal energy (dU) is related to a infinitesimal changes in volume (dV) and temperature (dT):

• Substituting:

• Gives:

TT

U

V

VV

UC

T

T V

U UdU dV dT

V T

T VdU dV C dT

Internal Pressure (πT)

• The internal pressure (πT) is a measure of the cohesive forces in the sample.

• Recall that:

• For a perfect gas, in which there are no interactions between the particles, the internal energy (U) is independent of the separation between the particles, and thus independent of the volume (V) of the sample.

• As a result, the internal energy (U) is independent of the volume (V) of the sample at constant temperature (T) .

• For an ideal gas:

T VdU dV C dT

0TT

U

V

Kkg

kJ Cp = Cv + R

For monatomic gases,

constants. are both and

R2

3R , C

2

5C vp

Enthalpy and Heat

• Enthalpy is defined: H = U + PV

• dH = dU + PdV + VdP

• at constant p,dH = dU + PdV = dqP – PdV + PdV

• dH = dqP or H = qP

Variation of H with T

TnCH

TdnCH

TdCnH

TdnCHd

mP

T

T

mP

T

T

mP

mP

,

,

,

,

2

1

2

1

pressure)constant (at

If Cp is independent of temperature between T1

and T2

Variation of H with T

12

21

222

1

2

2

2

11)(

/

)/(

;

/

2

1

2

1

2

1

2

1

TTncTTnbTnaH

TTdncTTdnbTdnaH

TdTcbTanH

then

TcbTaCTC

TdnCHd

T

T

T

T

T

T

T

T

pp

p

e.g. of function a is If

pressure)constant (at

Adiabatic Expansion

• dq = 0• dU = dw• for an ideal gas,

CVdT = – pexdV

• if reversible,pex = p = nRT/V

• therefore,CV(dT/T) = – nR(dV/V)

q

q

w

Reversible Adiabatic Expansion

i

f

i

fmV

mV

V

exV

V

VR

T

TC

V

dVR

T

dTC

dVV

nRTdTC

pdVdVpdTC

lnln,

,


R

VTVT

V

V

T

T

V

VR

T

TC

ic

fc

f

iR

C

i

f

i

f

i

fmV

if

mV

/C c where

lnln

mV,

,

,


iiff

ci

ci

cf

cf

i

c

iif

c

ff

ic

fc

VpVp

VpVp

VnR

VpV

nR

Vp

VTVTif

11

Polytropic Process Polytropic Process

PVn = C

Irreversible Adiabatic Expansion

ifexifV

exV

VVpTTC

dVpdTCdU

constant p assume ex

Adiabats vs. Isotherms

At any given pressure, Vadiabat < Visotherm because the gas cools during

reversible adiabatic expansion. In isothermal process when work is done, heat lost is replaced from the surrounding but in an adiabatic process it is not. In general which one has higher pressure for a given volume?

0

2

4

6

8

10

12

14

16

18

15 25 35 45 55 65

Volume

Pre

ss

ure

• Isotherm

• Adiabat

p

V

• Identify the nature of paths A, B, C, and D– Isobaric, isothermal, isovolumetric, and adiabatic

Lecture 27: Exercise 2Processes

p

V

AC

D

T1

T2

T3T4B

Equation of adiabatic process

1pV K

12TV K

13p T K

/p VC C K1 K2 K3 are constants

Calculation of adiabatic process

(1) The work of the adiabatic reversible process of ideal gas

2

1

dV

VW p V

2

1

= dV

V

KV

V ( )pV K

1 12 1

=1 1( )

(1 )K

V V

2 2 1 1=1

p V pVW

2 1( )1

nR T T

1 1 2 2p V p V K

Calculation of adiabatic process

(2) Work of adiabatic process

Cv(T2 –T1 )

because we do not introduce any other limitation conditions, this formula can be applied in adiabatic process of closed system which has fixed composing, need not always ideal gas, or reversible process.

W = U =

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kuliah KF1 (adiabatik1)