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Thermodynamics

Basic ConceptsSession2

Equilibrium state:

A system is said to be in thermodynamic equilibrium if it satisfies the condition

for thermal equilibrium, mechanical equilibrium and also chemical equilibrium. If it is in

equilibrium, there are no changes occurring or there is no process taking place.

Thermal equilibrium:

There should not be any temperature difference between different regions or

locations within the system. If there are, then there is no way a process of heat transfer

does not take place. Uniformity of temperature throughout the system is the requirement

for a system to be in thermal equilibrium.

Surroundings and the system may be at different temperatures and still system

may be in thermal equilibrium.

Mechanical equilibrium:

There should not be any pressure difference between different regions or locations

within the system. If there are, then there is no way a process of work transfer does not

take place. Uniformity of pressure throughout the system is the requirement for a system

to be in mechanical equilibrium.

Surroundings and the system may be at pressures and still system may be in

mechanical equilibrium.

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Chemical equilibrium:

There should not be any chemical reaction taking place anywhere in the system,

then it is said to be in chemical equilibrium. Uniformity of chemical potential throughoutthe system is the requirement for a system to be in chemical equilibrium.

Surroundings and the system may have different chemical potential and still

system may be in chemical equilibrium.

Thermodynamic process:

A system in thermodynamic equilibrium is disturbed by imposing some driving

force; it undergoes changes to attain a state of new equilibrium. Whatever is happening to

the system between these two equilibrium state is called a process. It may be represented

by a path which is the locus all the states in between on a p-V diagram as shown in the

figure below.

For a system of gas in piston and cylinder arrangement which is in equilibrium, altering

pressure on the piston may be driving force which triggers a process shown above in

which the volume decreases and pressure increases. This happens until the increasing

pressure of the gas equalizes that of the surroundings. If we locate the values of all

intermediate states, we get the path on a p-V diagram.

p

V

1

2

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Phase rule:

The two gas samples below have the same density, viscosity and all other intensiveproperties.

1 m3 of nitrogen at a pressure of 2 atmosphere and 300 K

2 m3 of nitrogen at a pressure of 2 atmosphere and 300 K

If a gas behaves ideally, then

RT

p

V

n

nRTpV

If M is the molecular weight of the gas, then

RT

pM

V

nM

V

m

RT

pM

Thus the density of an ideal gas depends upon only temperature and pressure as all other

quantities are constants. Since p and Tare same for the above nitrogen samples, density is

same. If we take out 1 cc of sample from any of those two, by observing only this 1 cc

sample we can never say from where we took the sample. This means to say the samples

are exactly same and indistinguishable. They are said to be in the same state.

In order to define this state of nitrogen, we need only T and p. Thus we need minimum

two variables to specify the state. This number is given by Gibbs phase rule which is

given by

NF 2

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where

F : degrees of freedom

: Number of phases

N : Number of components

For the above example, number of phases is one; number of components is one therefore

the degrees of freedom are two. For a system containing liquid water and its vapor in

equilibrium, we get the degrees of freedom to be one.

Following is the phase diagram of water which describes in what phase or phases

it can exist for different temperature and temperature.

T

p

Liquid

Solid

Vapor

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For the system to have two phases, if we mention the temperature alone given by

the vertical line, the pressure has to be the one given by horizontal line. Given the

pressure, its temperature gets fixed. Thus we have a freedom of fixing only one of them

which amounts to say degrees of freedom is one.

Heat reservoirs:

If the temperature of the system does not change if we remove a finite quantity of

heat from it, then the system is said to be heat reservoir. If the temperature of the system

does not change if we add a finite quantity of heat to it, then the system is said to be heat

sink.

Ocean can be made to act either as heat reservoir or heat sink.

Heat Engine:

Work and heat are forms of energy and are inter-convertible. Any device which

converts continuous supply of heat into useful work continuously is called heat engine.

For any system to undergo continuous process, it should be cyclic. The detailed

mathematical treatment of heat engines will follow in 5th

chapter on second law of

thermodynamics.

Irreversible process:

If a thermodynamic process takes place in such a way that we can retrace the path

exactly, the process is called reversible. Consider a piston and cylinder arrangement with

piston free to move at some pressure and temperature in equilibrium. The pressure of the

gas is balanced by a pressure equal to sum of atmospheric pressure and the weight on the

piston pan as shown. If the weight on the piston is reduced, then the piston moves up. Let

us just displace the part of the weight horizontally. This involves work. The piston moves

up as it is free to move until the pressures again become equal.

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Following is the p-V diagram for the process.

State -2

p

2

1

V

State -1

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Looking at the sequencing of the events, it is

1. Removal of part of weight on the piston which takes some work.

2. Moving of piston upward following some path on p-V diagram as shown.

Reaching a new steady position called state2.

Reversal of these events will mean

1. Piston moving downward from state-2 to state-1.

2. Weight moving on to the piston.

Can this reversal be possible? During expansion step, the system does work on the

surroundings. In reverse then, the surroundings should do the work at state 2. This is

not possible as the system and the surroundings have the same pressure. Exact reversing

is not possible. The process of bringing the weight on the piston pan is also not possible

as we need to do only by moving horizontally. The pan level is higher than that of the

weight. This requires extra work to be done. Further, in moving the weight work was

done on the weight. In reverse then, the weight should do the work, go and sit on the pan!

Clearly this is ridiculous which is not possible.

In order for a process to be reversible, the driving force must be infinitesimally small. If

we remove the weight bit by bit and place it horizontally, every bit would be placed one

above the other and then piston moves upward. At any point, the piston and the bit

removed are at the same level. As a result, at any point, we can move the bit horizontally,

making the piston move a bit down where the next bit of weight is available at the same

level. Reversing is thus possible.

However there is one work that can never be reversed even in this process. That is the

work done on the bit to move it horizontally. But this is less irreversible compared to the

earlier process where large part of the weight was removed. Look at the state-2, in order

to reverse; the weight has to be lifted by some vertical distance which is missing in the bit

by bit process. We can only strive to make a process only closer to reversibility.