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All the limitations of the first law of thermodynamics can be remove by the second law of thermodynamics. This law is generalisation of certain experiences about heat engines and refrigerators. It has been stated in a number of ways, but all the statements are logically equivalent to one another. (1) Statements of the law (i) Kelvin statement : “It is impossible to derive a continuous supply of work by cooling a body to a temperature lower than that of the coldest of its surroundings.” (ii) Clausius statement : “It is impossible for a self acting machine, unaided by any external agency, to transfer heat from one body to another at a higher temperature or Heat cannot itself pass from a colder body to a hotter body, but tends invariably towards a lower thermal level.” (iii) Ostwald statement : “It is impossible to construct a machine functioning in cycle which can convert heat completely into equivalent amount of work without producing changes elsewhere, i.e., perpetual motions are not allowed.” (iv) Carnot statement : “It is impossible to take heat from a hot reservoir and convert it completely into work by a cyclic process without transferring a part of it to a cold reservoir.” (2) Proof of the law : No rigorous proof is available for the second law. The formulation of the second law is based upon the observations and has yet to be disproved. No deviations of this law have so far been reported. However, the law is applicable to cyclic processes only.

A process which can take place by itself under the given set of conditions once it has been initiated if necessary, is said to be a spontaneous process. In other words, a spontaneous process is a process that can occur without work being done on it. The spontaneous processes are also called feasible or probable processes. On the other hand, the processes which are forbidden and are made to take place only by supplying energy continuously from outside the system are called non-spontaneous processes. In other words, non spontaneous processes can be brought about by doing work.  Examples of Spontaneous and Non-spontaneous processes  (1) The diffusion of the solute from a concentrated solution to a dilute solution occurs when these are brought into contact is spontaneous process.  (2) Mixing of different gases is spontaneous process.  (3) Heat flows from a hot reservoir to a cold reservoir is spontaneous process.  (4) Electricity flows from high potential to low potential is spontaneous process.  (5) Expansion of an ideal gas into vacuum through a pinhole is spontaneous process.  All the above spontaneous processes becomes non-spontaneous when we reverse them by doing work.  Spontaneous process and Enthalpy change : A spontaneous process is accompanied by decrease in internal energy or enthalpy, i.e., work can be obtained by the spontaneous process. It indicates that only exothermic reactions are spontaneous. But the melting of ice and evaporation of water are endothermic processes which also proceeds spontaneously. It means, there is some other factor in addition to enthalpy change \[(\Delta H)\] which explains the spontaneous nature of the system. This factor is entropy.

(1) Isothermal Expansion : For an isothermal expansion, \[\Delta T=0\]; \[\Delta E=\]0. According to first law of thermodynamics, \[\Delta E=q+w\]    \[\therefore \,q=-w\] This shows that in isothermal expansion, the work is done by the system at the expense of heat absorbed. Since for isothermal process, \[\Delta E\] and \[\Delta T\] are zero respectively, hence, \[\Delta H=0\] (i) Work done in reversible isothermal expansion :  Consider an ideal gas enclosed in a cylinder fitted with a weightless and frictionless piston. The cylinder is not insulated. The external pressure, \[{{P}_{ext}}\] is equal to pressure of the gas, \[{{P}_{gas}}\]. \[{{P}_{ext}}={{P}_{gas}}=P\] If the external pressure is decreased by an infinitesimal amount dP, the gas will expand by an infinitesimal volume, dV. As a result of expansion, the pressure of the gas within the cylinder falls to \[{{P}_{gas}}-dP\], i.e., it becomes again equal to the external pressure and, thus, the piston comes to rest. Such a process is repeated for a number of times, i.e., in each step the gas expands by a volume dV.                                      Since the system is in thermal equilibrium with the surroundings, the infinitesimally small cooling produced due to expansion is balanced by the absorption of heat from the surroundings and the temperature remains constant throughout the expansion. The work done by the gas in each step of expansion can be given as,      \[{{d}_{w}}=-({{P}_{ext}}-dP)dV=-{{P}_{ext}}.dV-dP\ .\ dV\] \[dP.dV,\] the product of two infinitesimal quantities, is negligible. The total amount of work done by the isothermal reversible expansion of the ideal gas from volume \[{{V}_{1}}\] to volume \[{{V}_{2}}\] is, given as, \[w=-nRT{{\log }_{e}}\frac{{{V}_{2}}}{{{V}_{1}}}\] or \[w=-2.303nRT{{\log }_{10}}\frac{{{V}_{2}}}{{{V}_{1}}}\]           At constant temperature, according to Boyle’s law, \[{{P}_{1}}{{V}_{1}}={{P}_{2}}{{V}_{2}}\] or \[\frac{{{V}_{2}}}{{{V}_{1}}}=\frac{{{P}_{1}}}{{{P}_{2}}}\] So,  \[w=-2.303nRT{{\log }_{10}}\frac{{{P}_{1}}}{{{P}_{2}}}\]            Isothermal compression work of an ideal gas may be derived similarly and it has exactly the same value with positive sign. \[{{w}_{compression}}=2.303nRT\log \frac{{{V}_{1}}}{{{V}_{2}}}=2.303nRT\log \frac{{{P}_{2}}}{{{P}_{1}}}\] (ii) Work done in irreversible isothermal expansion : Two types of irreversible isothermal expansions are observed, i.e., (a) Free expansion and (b) Intermediate expansion. In free expansion, the external pressure is zero, i.e., work done is zero when gas expands in vacuum. In intermediate expansion, the external pressure is less than gas pressure. So, the work done when volume changes from \[{{V}_{1}}\] to \[{{V}_{2}}\] is given by \[w=-\int_{{{V}_{1}}}^{{{V}_{2}}}{{{P}_{ext}}\times dV}=-{{P}_{ext}}({{V}_{2}}-{{V}_{1}})\] Since \[{{P}_{ext}}\] is less than the pressure of the gas, the work done during intermediate expansion is numerically less than the work done during reversible isothermal expansion in which \[{{P}_{ext}}\] is almost equal to \[{{P}_{gas}}\]. (2) Adiabatic Expansion : In adiabatic expansion, no heat is allowed to enter or leave the system, hence, \[q=0\]. According to first law of thermodynamics, \[\Delta E=q+w\]   \[\therefore \,\ \ \ \Delta E=w\] work is done by the gas during expansion at the expense of internal energy. In expansion, \[\Delta E\] decreases while in compression \[\Delta E\] increases. The molar specific heat capacity at more...

(1) Specific heat (or specific heat capacity) of a substance is the quantity of heat (in calories, joules, kcal, or kilo joules) required to raise the temperature of 1g of that substance through \[{{1}^{o}}C\]. It can be measured at constant pressure \[({{c}_{p}})\] and at constant volume \[({{c}_{v}})\]. (2) Molar heat capacity of a substance is the quantity of heat required to raise the temperature of 1 mole of the substance by \[{{1}^{o}}C\]. \ Molar heat capacity = Specific heat capacity ´ Molecular weight, i.e.,\[{{C}_{v}}={{c}_{v}}\times M\] and \[{{C}_{p}}={{c}_{p}}\times M\]. (3) Since gases on heating show considerable tendency towards expansion if heated under constant pressure conditions, an additional energy has to be supplied for raising its temperature by \[{{1}^{o}}C\] relative to that required under constant volume conditions, i.e., \[{{C}_{p}}>{{C}_{v}}\] or \[{{C}_{p}}={{C}_{v}}+\text{Work done in expansion, }P\Delta V(=R)\] where, \[{{C}_{p}}=\] molar heat capacity at constant pressure \[{{C}_{v}}=\] molar heat capacity at constant volume. (4) Some useful relations of Cp and Cv (i) \[{{C}_{p}}-{{C}_{v}}=R=2\,calories=8.314J\] (ii) \[{{C}_{v}}=\frac{3}{2}R\] (for monoatomic gas) and \[{{C}_{v}}=\frac{3}{2}+x\] (for di and polyatomic gas), where x varies from gas to gas. (iii) \[\frac{{{C}_{p}}}{{{C}_{v}}}=\gamma \] (Ratio of molar capacities) (iv) For monoatomic gas, \[{{C}_{v}}=3\,calories\] whereas, \[{{C}_{p}}={{C}_{v}}+R=5calories\] (v) For monoatomic gas, \[(\gamma )=\frac{{{C}_{p}}}{{{C}_{v}}}=\frac{\frac{5}{2}R}{\frac{3}{2}R}=1.66\] (vi) For diatomic gas \[(\gamma )=\frac{{{C}_{p}}}{{{C}_{v}}}=\frac{\frac{7}{2}R}{\frac{5}{2}R}=1.40\] (vii) For triatomic gas \[(\gamma )=\frac{{{C}_{p}}}{{{C}_{v}}}=\frac{8R}{6R}=1.33\]

Heat content of a system at constant pressure is called enthalpy denoted by ‘H’. From first law of thermodynamics, \[q=E+PV\]        ……….(i) Heat change at constant pressure can be given as \[\Delta q=\Delta E+P\Delta V\]                                                ……….(ii) At constant pressure heat can be replaced at enthalpy. \[\Delta H=\Delta E+P\Delta V\]                                                                ………(iii) \[\therefore \,\Delta H=\] Heat change or heat of reaction (in chemical process) at constant pressure \[\Delta E=\] Heat change or heat of reaction at constant volume. In case of solids and liquids participating in a reaction, \[\Delta H=\Delta E\,(P\Delta V\approx 0)\] Difference between \[\Delta H\] and \[\Delta E\] is significant when gases are involved in chemical reaction. \[\Delta H=\Delta E+P\Delta V\] \[\Delta H=\Delta E+\Delta nRT\] \[P\Delta V=\Delta nRT\] Here, \[\Delta n=\] nP – nR

Helmholtz and Robert Mayer proposed first law of thermodynamics. This law is also known as law of conservation of energy. It states that, “Energy can neither be created nor destroyed although it can be converted from one form into another.” \[{{E}_{2}}-{{E}_{1}}=\]\[\Delta E\,=q+w\] i.e. (Change in internal energy) = (Heat added to the system) +(Work done on the system) If a system does work (w) on the surroundings, its internal energy decreases. In this case,  \[\Delta E=q+(-w)=q-w\] i.e.(Change in internal energy)=(Heat added to the system) – (work done by the system) The relationship between internal energy, work and heat is a mathematical statement of first law of thermodynamics.         

This law forms the basis of concept of temperature. This law can be stated as follows,             "If a system A is in thermal equilibrium with a system C and if B is also in thermal equilibrium with system C, then A and B are in thermal equilibrium with each other whatever the composition of the system."                                                               

(1) Internal energy (E) : “Every system having some quantity of matter is associated with a definite amount of energy. This energy is known as internal energy.” \[E={{E}_{\text{translational}}}+{{E}_{\text{rotational}}}+{{E}_{\text{vibrational}}}+{{E}_{\text{bonding}}}+{{E}_{\text{electronic}}}+......\] (i) Characteristics of internal energy (a) Internal energy of a system is an extensive property. (b) Internal energy is a state property. (c) The change in the internal energy does not depend on the path by which the final state is reached. (d) There is no change in internal energy in a cyclic process. (e) The internal energy of an ideal gas is a function of temperature only. (f) Internal energy of a system depends upon the quantity of substance, its chemical nature, temperature, pressure and volume. (g) The unit of E is ergs in CGS or joules in SI 1 Joule = \[{{10}^{7}}\] ergs. (ii) Change in internal energy (\[\Delta E\]) : It is neither possible nor necessary to calculate the absolute value of internal energy of a system then,\[\]\[\Delta E={{E}_{f}}-{{E}_{in}}\] ; \[\Delta E\] is positive if \[{{E}_{f}}>{{E}_{in}}\] and negative if \[{{E}_{f}}<{{E}_{in}}\]. (2) Heat (q) and work (w) : The energy of a system may increase or decrease in several ways but two common ways are heat and work. Heat is a form of energy. It flows from one system to another because of the difference in temperature between them. Heat flows from higher temperature to lower temperature. Therefore, it is regarded as energy on the move. Work is said  to be performed if the point of application of force is displaced in the direction of the force. It is equal to the force multiplied by the displacement (distance through which the force acts). There are three main types of work which we generally come across. These are, Gravitational work, electrical work and mechanical work. Mechanical work = Force \[\times \] displacement = F.d Electrical work = potential difference \[\times \] charge = V.q Gravitational work = mgh (i) Units of heat and work : The heat changes are measured in calories (cal), Kilo calories (kcal), joules (J) or kilo joules (kJ). These are related as, 1 cal = 4.184 J; 1kcal = 4.184kJ The S.I. unit of heat is joule (J) or kilojoule. The Joule (J) is equal to Newton – metre (1 J= 1 Nm). Work is measured in terms of ergs or joules. The S.I. unit of work is Joule. 1 Joule = \[{{10}^{7}}\] ergs = 0.2390 cal. 1 cal   > 1 joule > 1 erg (ii) Sign conventions for heat and work Heat absorbed by the system = q positive Heat evolved by the system = q negative Work done on the system    = w positive Work done by the system    = w negative.  

           (1) System, surroundings and Boundary : A specified part of the universe which is under observation is called the system and the remaining portion of the universe which is not a part of the system is called the surroundings.            The system and the surroundings are separated by real or imaginary boundaries. The boundary also defines the limits of the system. The system and the surroundings can interact across the boundary.            (2) Types of systems            (i) Isolated system : This type of system has no interaction with its surroundings. The boundary is sealed and insulated. Neither matter nor energy can be exchanged with surrounding. A substance contained in an ideal thermos flask is an example of an isolated system.            (ii) Closed system : This type of system can exchange energy in the form of heat, work or radiations but not matter with its surroundings. The boundary between system and surroundings is sealed but not insulated. For example, liquid in contact with vapour in a sealed tube and pressure cooker.            (iii) Open system : This type of system can exchange matter as well as energy with its surroundings. The boundary is neither sealed nor insulated. Sodium reacting with water in an open beaker is an example of open system. (iv) Homogeneous system : A system is said to be homogeneous when it is completely uniform throughout. A homogeneous system is made of one phase only. Examples: a pure single solid, liquid or gas, mixture of gases and a true solution.            (v) Heterogeneous system : A system is said to be heterogeneous when it is not uniform throughout, i.e., it consist of two or more phases. Examples : ice in contact with water, two or more immiscible liquids, insoluble solid in contact with a liquid, a liquid in contact with vapour, etc.            (vi) Macroscopic system : A macroscopic system is one in which there are a large number of particles (may be molecules, atoms, ions etc. )            (3) Macroscopic properties of the system            Thermodynamics deals with matter in terms of bulk (large number of chemical species) behaviour. The properties of the system which arise from the bulk behaviour of matter are called macroscopic properties. The common examples of macroscopic properties are pressure, volume, temperature, surface tension, viscosity, density, refractive index, etc.            The macroscopic properties can be subdivided into two types,            (i) Intensive properties : The properties which do not depend upon the quantity of matter present in the system or size of the system are called intensive properties.  Its examples are pressure, temperature, density, specific heat, surface tension, refractive index, viscosity, melting point, boiling point, volume per mole, concentration etc.            (ii) Extensive properties : The properties whose magnitude depends upon the quantity of matter present in the system are called extensive properties. Its examples are total mass, volume, internal energy, enthalpy, entropy etc. These properties are additive in nature.             Any extensive property if expressed as per mole or per more...

(1) System, surroundings and Boundary : A specified part of the universe which is under observation is called the system and the remaining portion of the universe which is not a part of the system is called the surroundings. The system and the surroundings are separated by real or imaginary boundaries. The boundary also defines the limits of the system. The system and the surroundings can interact across the boundary. (2) Types of systems (i) Isolated system : This type of system has no interaction with its surroundings. The boundary is sealed and insulated. Neither matter nor energy can be exchanged with surrounding. A substance contained in an ideal thermos flask is an example of an isolated system. (ii) Closed system : This type of system can exchange energy in the form of heat, work or radiations but not matter with its surroundings. The boundary between system and surroundings is sealed but not insulated. For example, liquid in contact with vapour in a sealed tube and pressure cooker. (iii) Open system : This type of system can exchange matter as well as energy with its surroundings. The boundary is neither sealed nor insulated. Sodium reacting with water in an open beaker is an example of open system. (iv) Homogeneous system : A system is said to be homogeneous when it is completely uniform throughout. A homogeneous system is made of one phase only. Examples: a pure single solid, liquid or gas, mixture of gases and a true solution. (v) Heterogeneous system : A system is said to be heterogeneous when it is not uniform throughout, i.e., it consist of two or more phases. Examples : ice in contact with water, two or more immiscible liquids, insoluble solid in contact with a liquid, a liquid in contact with vapour, etc. (vi) Macroscopic system : A macroscopic system is one in which there are a large number of particles (may be molecules, atoms, ions etc. ) (3) Macroscopic properties of the system Thermodynamics deals with matter in terms of bulk (large number of chemical species) behaviour. The properties of the system which arise from the bulk behaviour of matter are called macroscopic properties. The common examples of macroscopic properties are pressure, volume, temperature, surface tension, viscosity, density, refractive index, etc. The macroscopic properties can be subdivided into two types, (i) Intensive properties : The properties which do not depend upon the quantity of matter present in the system or size of the system are called intensive properties.  Its examples are pressure, temperature, density, specific heat, surface tension, refractive index, viscosity, melting point, boiling point, volume per mole, concentration etc. (ii) Extensive properties : The properties whose magnitude depends upon the quantity of matter present in the system are called extensive properties. Its examples are total mass, volume, internal energy, enthalpy, entropy etc. These properties are additive in nature. Any extensive property if expressed as per mole or per gram becomes an intensive property. (4) State of a system and State Variables Macroscopic more...