Unlike the internal energy and heat content ,the work obtainable when a system undergoes change depends not only on the initial and final states but also on how the change takes place .The work performed by a system can vary all the way from zero, “in case of expansion into vacuum ,up to a maximum under specified conditions .•Any process in which the driving force is only infinitesimally greater than the opposing force ,and which canbe reversed by increasing the opposing force by an infinitesimal amount constitute reversible process .•All naturally occurring process are irreversible•Reversibility can be approached in galvanic cells .
Reversibility and maximum work
•The amount of work a system has to perform to give certain change depends on the opposition the system experiences to the change, the greater that resistance is, the more work must be done by the system.
•Consider the expansion of an ideal gas against a pressure P through an infinitesimal volume change dv, the work done is zero , if P is zero, however as P increased more and more work has to be done as the pressure approaches that of the gas ifself.
•It is evident that the work which may performed by a system is a maximum when the opposing pressure P differs only infinitesimally from the internal pressure of the gas itself. Thus maximum work is obtainable only from a system when the change taking place in it is entirely reversible.
since w = ∫ Pdv
for reversible process the external pressure is at all times only infinitesimally lower than the pressure of the gas itself, we may substitute P = nRT/ v
So Wm= ∫v1v2 nRTdv/v
• Wm = nRT ∫v1v2 dv/v = nRT ln v2/v1
alternatively Wm = nRT ln p1/p2
Maximum work of adiabatic expansion.
The expression in question is arrived at as:
Differentiate the expression pvγ = constant.
γ pvγ-1 dv + vγdp = 0 dividing by vγ-1
γ pdv + v dp = 0
v dp = - γ pdv
complete differentiation of pv = nRT gives:
P dv + v dp = nRT
On substitution of the expression for v dp
P dv - γ P dv = nR dT
P dv ( 1- γ) = nR dT
P dv = nRdT / ( 1- γ)
Wm = ∫v1v2 p dv = ∫T1T2 nR dT / ( 1- γ)
= nR ( T2 – T1) / ( 1- γ)
T2> T1 Wm is negative and work is done on the gas, when work is done by the system
T2< T1 and Wm is positive.
The maximum work function A
•We have seen that the amount of work obtainable from a process depends on the manner in which the work has been performed. Under isothermal and reversible conditions a definite path of passing from the initial to the final state along which the maximum work done is definite and dependent only on the two states.
•At constant temperature, when the maximum work being a function of the states as the internal energy E and heat content H.
•Therefore , we may think of a system as possessing in each state a certain amount of maximum work content A, called (the Helmholtez free energy), when the system passes from one state to another, the change in the work function ∆ A is equal;
∆ A = A2 - A1
∆ A > 0 means increase in the work content
∆ A < 0 means decrease in the work content
Thus Wm = - ∆A
From the first law; ∆E = qr - Wm
= qr + ∆A
The joule – Thomson effect
•For an ideal gas, pv product is a constant , if this gas expands under adiabatic conditions into a vacuum, then;
q = 0 w = 0 ∆E = 0
i.e ∆E for the gas remains constant as vp and consequently the temperature. This is equivalent to say” At constant temperature the internal energy of an ideal gas is independent of the volume the gas occupies or ( ∂ E / ∂v)T = 0
With real gases the situation is different;
Joule – Thomson experiment
By applying pressure on the piston on the left slowly enough so as not to change the pressure p1, a volume of gas v1 was forced slowly through the pours plug and allowed then to expand to the pressure p2 and volume v2by moving the piston on the right. At left piston At right piston
Work done is – p1v1 work done is p2v2
The net work w = p2v2– p1v1
q = 0 since the process is adiabatic
∆E = E2 – E1 = - w = - (p2v2– p1v1 )
E2+ p2v2 = E1 + p1v1
H2 = H1 ∆H = 0
i.e. the process was conducted at constant enthalpy.
Under these conditions joule - Thomson observed near room temperatures that all gases show cooling except hydrogen actually became warmer, the extent of the temperature change was found to depend on the initial temperature and pressure of the gas.
•The magnitude of the observed effects controlled by the joule – Thomson coefficient µ which is defined as:
‘The number of degrees temperature change produced by atmosphere drop in pressure under constant enthalpy”. µ = (∂T / ∂p)H
µ positive cooling
µ negative heating
Hydrogen and helium can be cooled adiabatically if they are first brought to a sufficient low temperature, this temperature is called inversion temperature, namely, the temperature at which the gas exhibit neither cooling nor heating.
This effect is of great importance in liquefaction of gases.
The carnot cycle
•A question of great significance to how extent heat is convertible to other forms of energy which may utilize to do work, experience has shown that operating heat engines which absorb heat at temperature T2 and reject the waste heat at a lower temperature T1, can convert only a fraction of the absorbed heat into work.
•Theoretical consideration show that even an ideal engine , operating under ideal conditions, would be able to convert only a certain fraction of the absorbed heat into work and that this fraction depend only on the operating tempe.
•To establish the above deductions, let us consider the sequence of operation called a carnot cycle, which consists of four steps, two isothermal and two adiabatic.
W1 = nRT2 ln v1/v2 = q2 (a)
W2 = - ∆E = - ncv ( T1 –T2) (b)
W3 = nRT1 ln v4/v3 = - q1 ( c)
W4 = - ∆E = -ncv (T2 – T1)= ncv (T1- T2) (d)
Wm = w1 + w2 + w3 + w4
= nRT2ln v2 /v1 + nRT1 ln v4/v3 = q2-q1 (A)
Division of equation (A) by q2 yields:
Wm/q2 = q2 – q1 /q2 =
nRT2 ln v1/v2 + nRT1 ln v4/v3 / nRT2 ln v1/v2(B)
Equation (B) can be simplified,since the points (p1v1) and (p3v3) lie on the same adiabatic ,
then: v1T2cv/R = v3T1cv/R
Similarly, the points (p2v2) and (p4v4) lie on the same adiabatic then:,
V2 T2cv/R = v4T1cv/R
On dividing the first equation by the second we obtain: v1 /v2 = v3 /v4 consequently
ln v4 /v3 = - ln v1 /v2
substituting this value in equation (B) we get
W/q2 =RT2 ln v1 /v2-RT1 ln v1 /v2/RT2ln v1 /v2
= (T2 –T1) /T2
and wm = q2 ( T2-T1 / T2)
•Thus the maximum work that may be recovered from a system during a reversible cyclical process is equal to the heat absorbed multiplied by the ratio (T2-T1/T2 )
•The ratio of wm /q2 is called the thermodynamic efficiency of the process.
•Thermodynamic efficiency must be the same for all the process operating under the given temperature conditions.
Theory of Indicators 
The ionic theory of solutions permitted the formulation of a logical conception of the action of indicators by W. Ostwald which for many years held its ground practically unchallenged; and even now the arguments originally advanced hold good, except for certain qualifications rendered necessary by more recent research. In the language of the ionic theory, an acid solution is one containing free hydrions, and an alkaline solution is one containing free hydroxidions. A neutral solution contains hydrions and hydroxidions in equal concentration; this is a consequence of the fact that pure water itself undergoes a certain dissociation, and several different methods show that in the purest water obtainable the concentration of the free hydrions and hydroxidions is 107 at 24°. Moreover, the law of mass-action (see Chemical Action) demands that the product of the concentrations of the hydrions and hydroxidions in any solution is constant at a given temperature, and we see from the above values that this constant is 1014. It follows, therefore, that the acidity or alkalinity of any solution can be expressed both in terms of hydrion or hydroxidion concentration. Many researches have been directed to classify acid and alkaline solutions according to the concentration of the hydrion. Conductivity determinations show that the maximum concentration of hydrion occurs in 5.8 - N nitric acid, where it has a value of about 2 -N, and the minimum occurs in 6.7N potassium hydroxide, where its value is 5 X I 015, that of the hydroxidion being about 2 - N. These figures apply to a temperature of 24 °. Bearing in mind the concentration of the ions in a neutral solution, it is seen that a scheme of seven grades of "neutrality," differing by successive powers of ten, may be formulated. The concentration of hydrion and hydrox idion in any solution may be determined by several independent methods, and it is therefore a simple matter to prepare solutions of definite ionic concentrations and to test these with the object of obtaining a list of indicators according to their sensitiveness. It is found that litmus responds to concentrations of io-- 6 H and 106 0H', a result which shows this dye to be the best indicator of true neutrality. Methyl orange responds to between - 4H and I 05 H - para-nitrophenol to between io - 5 H- and 106 Hand phenolphthalein to between r05 0H' and t06 0W. Salm (Zeit. Elektrochem., 1904, 10, p. 341) gives a list of twenty-seven indicators classified on this principle. Other papers bearing on this subject are Friedenthal, ibid., p. 113; Salessky, ibid., p. 204; Fels, ibid., p. 208; Scholtz, ibid., p. 549; M. Handa, Ber., 1909, 4 2, p. 3179.
A pH indicator is a halochromic chemical compound that is added in small amounts to a solution so that the pH (acidity or alkali nity) of the solution can be determined easily. Hence a pH indicator is a chemical detector for hydronium ions (H3O+) (or Hydrogen ions (H+) in the Arrhenius model). Normally, the indicator causes the color of the solution to change depending on the pH. Solutions with a pH value above 7.0 are alkali, and solutions with a pH value below 7.0 are acidic. Solutions with a pH value of 7.0 are neutral 
pH indicators themselves are frequently weak acids or bases. When introduced into a solution, they may bind to H+ (Hydrogen ion) or OH- (hydroxide) ions. The different electron configurations of the bound indicator causes the indicator's color to change, which allows the pH to be determined by the different colors. 
Many plants or plant parts contain chemicals from the naturally-colored anthocyanin family of compounds. They are red in acidic solutions and blue in basic. Extracting anthocyanins from red cabbage leaves or the skin of a lemon to form a crude acid-base indicator is a popular introductory chemistry demonstration.
