Thermodynamic variables Path Function State Function A I II B

W I

III 

W II



W III

(Path Function) (V B -V A ) I = (V B -V A ) II = (V B -V A ) III (state Function)

Between two states the change in a state variable is always the same regardless of which path the system travels.

a



b dV



V b



V a

Differential of a state function is called EXACT DIFFERENTIAL

a



b dW



W b



W a

Differential of a path function is called inexact differential.

y b b y a

II

a

I

x a x

a



b dz

 

a b ydx

 area I x b Path dependent hence inexact differential 

b a dz

 

a b ydx

 

x dy

 

b a d

(

x y

) area I  area II 

x b y b



x a y a

Does not depend on path hence exact differential

Simple test to see whether a differential is exact (Euler’s Criterion for exactness)

p



f

(

T

,

V

) is a state function then

dp

  

p T



V dT

  

p V T dV

With the condition   V     

p



T



V

  

T

   that

T

    

p



V T

  

V

Molar volume of an ideal gas

V m dV



m RT



P



V m



P



T dP

 

V



T m p dT dV m

 

T



RT P

2

RT P

2

P



dP

 

P R

2

R



dT P

 

P R P



T

State variables are also called state properties.

The state of a system is defined as the complete set of all its properties which can change during various specified processes.

When a system is at equilibrium, its state is defined entirely by the state variables, and

not by the history of the system

. The properties of the system can be described by an equation of state which specifies the relationship between these variables.

State Variables P,T,V Cut into half P,T,V/2 P,T,V/2 P and T are intensive variables, V is an extensive variable The variables often form pairs such that their product has the dimensions of energy (e.g. pressure & volume in a gas). The intensive member plays the role of force and the extensive the role of displacement.

We can influence a system either by doing

work

(e.g. compression), or

thermally

(e.g. heat with a flame).

Work is done when an object is moved against an opposing force.

The energy of the system is its capacity to do work.

Heat is energy in transit due to temperature difference.

Work is transfer of energy that make use of organized motion.

When a system does work, it stimulates orderly motion in the surroundings.

Heat is the transfer of energy that makes use of unorganized molecular motion.

When energy is transferred to the surroundings as heat, the transfer stimulates disordered motion of the atoms in the surroundings.

Joule’s experiment Joule heated water by performing work on it, in this case by rotating a paddle wheel.

adiabatic He found that the temperature rise was dependent only on the amount of work but independent of how the work was performed (e.g. quickly or slowly, large or small paddle wheel).

Temperature rise means there is change in state.

The property of the system whose change is calculated in this way is called internal energy.



U



w adiabatic

Same change in state (temperature rise) can be achieved by allowing heat to flow in.

System in state 1 system Heat reservoir Heat conducting Wall Heat reservoir System in state 2 Heat reservoir 

U



q

(no work done)

Energy can be converted from one form to another, but it cannot be created or destroyed. 

U



q



w

Change in internal energy of a closed system is equal to the energy that passes through its boundary as heat or work.

For a infinitesi

dU

mal changes 

dq



dw

of state

•The first law contains three essential features : • It is a statement of the principal of conservation of energy.

• It requires the existence of the internal energy function.

• It leads to the definition of heat as energy in transit.

U

is a function of the state variables and can be written as

U



f

(

V

,

T

) But

Q

and

W

are not functions of the state so we cannot determine quantities like 

Q



P

or 

W



V

For an adiabatic system,

dq

  0

dU



dw

This means that work needed to change an adiabatic system from one specified state to another specified state is a state function.

w ad is a state function.



w ad



U f



U i

General expression for work

d

w

 

F

dz d

w dw w

    

p ex p ex A

d d

V z

 

V V i f p ex

d

V

(a) Free expansion (b) p ex =0, w=0 Expansion against constant pressure (Expansion of gas formed in a chemical reaction)

P 1 ,V 1 ,T P 1 P 2 P 1 P 2 P 1 P 2 V 1 V 1 V 1 h P 2 ,V 2 ,T V V V 2 2 2

P 1 P 2 V 1 V 2 For infinite number of step P 1 P 2 V 1 V 2 Infinite state expansion is called reversible process.

These infinite-step processes at constant temperature are reversible because the energy accumulated in the surroundings in the expansion is exactly the amount required to compress the gas back to the initial state.

P 1 P 2 V 1 V 2

h P 1 ,V 1 ,T P 1 P 2 V 1 P 1 ,V 1 ,T P 2 P 1 V 2 h P 2 ,V 2 ,T V 2 P 2 ,V 2 ,T V 1

Important points about reversible processes They can be reversed at any point in the process by making an infinitesimal change.

A reversible expansion or compression requires •A balancing of internal and external pressure.

•Time to reestablish equilibrium after each infinitesimal step.

•Absence of friction.

For the processes in the chemical industry, the greater the irreversiblity, the greater is the loss in capacity to do work. Every irreversibility has its cost.

Ways to approach reversibility

Heat may be transferred nearly reversibly if the temperature gradient across which it is transferred is made very small.

Electrical charge may be transferred nearly reversibly from a battery if a potentiometer is used so that the difference in electric potential is very small.

A liquid may be vaporized nearly reversibly if the pressure of vapor is made only very slightly less than the equilibrium vapor pressure.

P 1 ,V 1 ,T P 1 P 2 V 1 P 2 ,V 2 ,T P 1 P 2 V 1 h P 2 ,V 2 ,T =P 2 (V 2 -V 1 ) h V 2 P 1 ,V 1 ,T =-(P 1 (V 2 -V 1 )) V 2

P 1 ,V 1 ,T P 1 P 2 V 1 P 2 ,V 2 ,T P 1 P 2 V 1 h P 2 ,V 2 ,T =nRTln(P 1 /P 2 ) h V 2 P 1 ,V 1 ,T =-nRTln(P 1 /P 2 ) V 2

The variables often form pairs such that their product has the dimensions of energy). The intensive member plays the role of force and the extensive the role of displacement.

Type of Work Intensive variable Expansion Surface P  (surface tension) Elongation Electrical Extensive Variable V A F  (potential diff.) L Q

dU



dq



dw

exp ( PV kind ) 

dw e

Differential work -PdV  dA FdL  dQ

Heat

Heat is energy in transit due to temperature difference.

Mechanical definition= w

ad

-w

•If a quantity of heat is required to increase the temperature of a body by

dT

, the 

C

  

q

 

T dT

is defined to be •Since heat is an inexact differential, depending upon the way in which energy changes occur, then it is clear that there cannot be a unique heat capacity for a system either. • So the quantity of heat which flows in will depend upon the path of the transformation and there will be an infinite number of heat capacities.

Of the infinite possible number, it is customary to define two heat capacities. Heat capacity at constant volume

C V

and heat capacity at constant pressure

Cp

dq V



C V dT

C V is called heat capacity at constant volume.

C V can be determined by burning a known mass of substance that has known heat output. With C V known, it is simple to interpret an observed temperature rise as a release of heat Specific heat is essentially a measure of how thermally insensitive a substance is to the addition of energy.

Most processes that occur in the laboratory, on the surface of the earth, and in organisms do so under a constant pressure of one atmosphere Some of the energy supplied as heat to the system is returned to the surrounding as expansion work.

Specific heat is essentially a measure of how thermally insensitive a substance is to the addition of energy. •For solids and liquids

c V

and

c p

are very similar. Aluminium 900 J Kg -1 C -1 Wood 1700 J Kg-1 C-1 Water 4186 J Kg-1 C-1 •The high specific heat of water is the reason that coastal regions have milder climates than inland regions at the same latitude.

Important point about Internal energy Internal energy is the total of the kinetic energy of the constituent atoms or molecules due to their motion ( translational , rotational , vibrational ) and the potential energy associated with intermolecular forces. It includes the energy in all of the chemical bonds , and the energy of the free, conduction electrons in metals .

Important point about Internal energy

•

Internal

energy does not include the translational or rotational kinetic energy of a body

as a whole

.

• It also does not include the relativistic mass -energy equivalent

E

=

mc

2 .

• It excludes any potential energy a body may have because of its location in external gravitational or electrostatic field , although the potential energy it has in a field due to an moment induced does count. electric or magnetic dipole

dU



U U q

2

p

 

dq q p

 

dw P



V

(at constant  

U

1 (

U

2  

q p



PV

2

P

(

V

2 )  ( 

U

1

V

1  )

PV

1 ) 

H

2 

H

1 P) Enthalpy is a state function.

Enthalpy is an extensive quantity.

The change in enthalpy is equal to the heat absorbed in a process at constant pressure if the only work done is reversible pressure-volume work.

H dH

 

f

(

P

,

T

) 

H



T



V dT

  

H P

At constant

dH

 

H



T

pressure,

P dT dH



dq P

 

H



T P dT



C p dT



T dP