Thermodynamics

Thermodynamics

Vijay Ratna

Thermodynamics deals with the flow of energy. It explains the quantitative relationships between different forms of energy as energy changes from one form to another. The study of thermodynamics consists of understanding (1) Basic definitions (2) First Law  (3) Second Law (4) Third Law and (5) Free energy functions. “Energy” and its transfer are applicable in determining the fate of simple chemical processes to describing very complex behavior  of biological cells.

I. Basic Definitions :

1. System : A “system” is a well defined part of the universe that one is interested in studying.

2. Open System : An open system is one from which energy and matter can be exchanged with the surroundings.

3. Closed System : A closed system is one from which there is no exchange of matter with the surroundings.

4. Isolated system : An isolated system is one from which neither energy transfer nor mass transfer can take place.

5. “Work” is a transfer of energy that can be used to change some height or some weight some where in the surroundings.

6. Heat is a transfer of energy resulting from a temperature difference between the system and the surroundings.

7. A thermodynamic system is said to be in a certain state when all its properties are fixed.

8. The fundamental properties which determine the state of a system are pressure (p), temperature (t), Volume (v), mass and composition. Since a change in the magnitude of such properties alters the state of the system, these are referred to as state variables or state functions or thermodynamic parameters. The variables P and T which must be necessarily specified to define the state of a system are designated as Independent state variables. The remaining state variable (v) which depends on the value of P and T is called Dependent State Variable.

9. A system in which the state variables have constant values throughout the system is said to be in a state of thermodynamic equilibrium.

10. A system in which the state variables have different values in different parts of the system is said to be in a non-equilibrium state.

11. Energy can be considered as the product of an intensity factor and the differential of an extensive property.

12. Intensive property is independent of the quantity of material.

13. Extensive property is proportional to the mass of the system.

14. P,V, and T are interrelated in the form of an algebric relationship called the equation of state. Thus for one mole of a pure gas, the equation of state is PV = RT.

16. PV work or expansion work :

The work done by a gas in expanding against constant external pressure (by increase in the termperature) is

17. Internal energy : Internal energy results from the motions of the molecules, electrons, and nuclei in a system and depends on the measurable properties, Pressure, volume and temperature. Any two of these variables must be specified in order to define the internal energy.

18. Enthalpy : Heat content per unit mass of substance.

19. Entropy : When Q_rev (Heat transferred in a reversible process), a path dependent property, is divided by T, (Temperature) a new path-independent, property is generated called entropy. It is defined as

Thus, the term Q_Hot/T_Hot is known as the entropy change of the reversible process at T_Hot and Q_cold/T_cold is the entropy change of the reversible process at T_cold. Entropy is a measure of the disorderliness of the system.

20. Free Energy Function : Free energy functions help us in determining the spontaneity of a chemical reaction or phase change. The functions for predicting spontaneity are

1. Isolated system: dS > 0

2. Isothermal and isochoric system: dA < 0

3. Isothermal and isobaric: dG< 0

4. Constant volume and entropy:dE < 0

First Law Of Thermodynamics

The first law is a statement of the conservation of energy. It states that, although energy can be transformed from one kind into another, it cannot be created or destroyed. The total energy of a system and its immediate surroundings remains constant during any operation.

According to the first law, the effects of Q and W in a given system during a transformation from an initial thermodynamic state to a final thermodynamic state are related to an intrinsic property of the system called the internal energy;

Where E₂ is the nternal energy of the system in its final state and E₁ is the internal energy of the system and its initial state, Q is the heat and W is the work.

The change in internal energy does not depend on the path taken.

The work done by a system in an isothermal expansion process is at a maximum when it is done reversibly.

Modified First Law Equations for processes occurring under various conditions.

Conditon                                Modification of First Law

(a) Constant heat (adiabatic)                    dE = dW

(b) Reversible process at a constant             dW =Wmax

 Temperature (Isothermal)

© Ideal gas at a constant temperature            dE = O

    (Isothermal)                                 dq = -dw

(d) Constant volume Isometric                   dw = -Pdv = O

      Or Isochoric                               dE = Qv

(e) Constant pressure (Isobaric)                dH = Qp

                                              dE = dH –Pdv

Metabolism and the first law: Human beings and other animals do work. Work is done when a person walks or runs or lifts a heavy object work requires energy. Energy is also needed for growth – to make new cells, and to replace old cells that have died. A great many energy – transforming processes occur within an organism, and they are referred to as metabolism.

We can apply the first law of thermodynamics ΔE = Q –W to an organism, say the human body. Work W is done by the body, and this would result in a decrease in the body’s internal energy (and temperature) which must be replenished. The body’s internal energy is not maintained by a flow of heat Q into the body. Normally, the body is at a higher temperature that its surroundings, so that heat usually flows out of the body. Even on a very hot day when heat is absorbed, the body has no way of utilizing this heat to support it vital processes. What then is the source of energy? It is the internal energy (chemical potential energy) stored in foods. Now in a closed system the internal energy changes only as a result of heat flow or work done; in an open system, such as an animal, internal energy itself can flow into or out of the system. When we eat food, we are bringing internal energy into our bodies directly, which thus increases the total internal energy E in our bodies. This energy eventually goes into work and heat flows form the body according to the first law.

The Second Law of Thermodynamics

1.  
   1. The second law refers to the probability of the occurrence of a process based on the observed tendency of a system to approach a state of energy equilibrium.
   2. A steam engine can do work only with a fall in temperature and a flow of heat to the lower temperature. No useful work can be obtained from heat at constant temperature.
   3. Heat is isothermally unavailable for work; it can never be converted completely into work. The second law provides a criterion for deciding whether a process follows the natural or spontaneous direction.
   4. The entropy of an isolated system never decreases. It can only stay the same or increase.
   5. In general, spontaneous processes at constant temperature and pressure are accompanied by a loss in free energy, and greater entropy.
   6. Mechanical energy can be obtained from thermal energy only when heat is allowed to flow from a high temperature to a low temperature.
   1. In an irreversible process, the entropy change of the total system or universe  (a system and its surroundings) is always positive because ΔS_sun is always less than ΔS_syst in an irreversible process.



9.For any system and its surroundings or Universe,



There are two cases in which ΔS = 0

(a) a system in a reversible cyclic process and

(b)a system and its surroundings undergoing any reversible process.

ΔS_univ = Δ S_syst +Δ S_sun > O

and this can serve as a criterion of spontaneity of a real process.

Heat engines and refrigerators :

It is easy to produce thermal energy by doing work – for example, by simply rubbing your hands together briskly, or indeed in any frictional process. But to get work from thermal energy is more difficult, and the invention of a practical device to do this came only about 1700 with the development of the steam engine.

The basic idea behind any heat engine is that mechanical energy can be obtained from thermal energy only when heat is allowed to flow from a high temperature to a low temperature; in the process some of the heat can then be transformed to mechanical work. The high and low temperatures, T_H and T_L are called the operating temperatures of the engine. We will be interested only in engines that run in a repeating cycle (that is, the system returns repeatedly to its starting point) and thus can run continuously.

12.6  Schematic diagram of a heat engine.



Carnot found that for an idealized reversible engine the efficiency could be written in terms of the operating temperatures of the engine T_H and T_L (where T_H>T_L) specified in degrees Kelvin :



Real engines cannot have an efficiency even this high because of losses due to friction and the like. Real engines that are well desgined reach 60 to 80 percent of the Carnot efficiency.

The Third Law of Thermodynamics

The entrory of a substance varies directly with temperature. The lower the temperatue, the lower the entropy. For example, water above 100 at one atmosphere exists as a gas and has higher entropy (higher disorder). The water molecules are free to roam about in the entire container: when the system is cooled, the water vapour condenses to form a liquid. Now the water molecules are confined below the liquid level but still can move about somewhat freely. Thus the entropy of the system has decreased. On further cooling, water molecules join together to form ice crystal. The water molecules in the crystal are highly ordered and entropy of the system is very low.

If we cool the solid crystal still further the vibration of molecules held in the crystal lattice gets slower and they have very little freedom of movement (very little disorder) and hence very small entropy. Finally at absolute zero all molecular vibration ceases and water molecules are in perfect order. Now the entropy of the system will be zero.



Entropy Decreases

Fig 9.4: Change of water vapour to liquid and then to solid crystals is accompanied by decrease of entropy with increasing order.



Molecular status in a solid crystal (Illustration of the Third Law).

The leads us to the statement of the third law of thermodynamics. “at absolute zero, the entropy of a pure crystal is also zero”.

Free Energy Function :

Helmholtz free energy is defined as

A = E – TS

Helmholtz free energy is the energy available to do pressure – volume work for reversible isothermal processes, or, a decrease in the Helmholtz free energy is equal to the capacity of the system to do work. For systems at constant volume and temperature, a change in state is spontaneous if and only if, there is a decrease in the Helmholtz free energy.

Gibbs free energy is defined as

G= E + PV-TS

A decrease in Gibbs free energy is equal to the nonpressure volume work done by the system. A direct application of the relationship between Gibbs free energy and non-PV work is used in potentiometry.

Standard Entropy :

From the third law, we know that the entropy of a pure crystal in zero at absolute zero (K). Therefore, it is possible by measurement and calculations to find the actual amount of entropy that substances possess at any temperature above 0K. It is referred to as absolute entropy.

The absolute entropy of a substance at 25C (298K) and one atmosphere pressure, is called the standard entropy; S^O.