The Second Law of Thermodynamics

• The second law of thermodynamics distinguishes between heat and work as forms of energy.
• In energy balance equations, both heat and work are included as additive terms.
• While a Joule of heat can be equivalent to a Joule of work in terms of energy units, there's a qualitative difference between them.

Work

• Work can be easily transformed into other forms of energy, such as potential energy (by elevation of weight), kinetic energy (acceleration of mass), and electrical energy (operation of motors).
• Work can be completely transformed into heat, as demonstrated by Joule's experiment.

Heat

• Continuous conversion of heat completely into work (mechanical or electrical) has not been achieved.
• Maximum conversion efficiencies usually do not exceed 40%.
• Heat is intrinsically less useful and less valuable than an equal quantity of work or electrical energy.
• The restriction on the complete conversion of heat into work is a central concept in the second law of thermodynamics.

Statements of the Second Law

• Statement 1: No device can operate in a way that its only effect is to convert heat absorbed by a system completely into work done by the system.
• Statement 2: No process is possible which consists solely in the transfer of heat from one temperature level to a higher one.

Explanation for Statement 1

• The first statement doesn't prohibit the conversion of heat into work, but it states that the process cannot leave both the system and its surroundings unchanged.
• Consider a system with an ideal gas in a piston/cylinder assembly expanding reversibly at constant temperature.
• ΔU = Q + W, and for an ideal gas, ΔU = 0, therefore, Q = -W.
• Heat absorbed from the surroundings is converted completely into work, which is transferred to the surroundings (reversible expansion of gas).
• While this appears to contradict the second law, there is a change in the system and surrounding such as lowering the pressure of the gas.

Sub-statements of 1

• It is impossible for a cyclic process to convert the heat absorbed by a system completely into work done by the system.

Explanation

• For the system described earlier the pressure of the gas soon reaches that of the surroundings, and expansion stops.
• Continuous production of work from heat by this method is therefore impossible.
• To comply with the first statement, energy from the surroundings must compress the gas back to its original pressure.
• This reverse process requires at least the amount of work gained from expansion. Therefore, the net work is zero.
• The second law does not prohibit the production of work from heat, but it places a limit on how much heat directed into a cyclic process can be converted into work.

Heat Engines

• The classical approach to the second law is based on the study of heat engines.
• Heat engines are devices or machines that produce work from heat in a cyclic process.
• An example is a steam power plant, where the working fluid (steam) periodically returns to its original state.
• Liquid water requires energy to boil into high-pressure steam in the boiler.
• Heat from fuel (combustion of fossil fuel or nuclear reaction) is transferred in the boiler to water.
• Energy is transferred as shaft work from steam to the surroundings by a turbine.
• The steam expands to reduced pressure and temperature.
• Exhaust steam from the turbine is condensed by transferring heat to the surrounding.
• Hot reservoirs result from the combustion chamber of fossil fuel or nuclear reactor.
• Cold reservoirs are created to represent the heat discarded to the surrounding.
• In operation, a working fluid of a heat engine absorbs heat |QH| from a hot reservoir which produces a net amount of work |W| and discards heat |QC| to a cold reservoir, and then it returns to its initial state.

Thermal Efficiency

• Defined as η = net work output / heat absorbed.
• η = |W| / |QH| = (|QH| - |QC|) / |QH| = 1 - |QC| / |QH|.
• For η to be unity (100% thermal efficiency), |QC| must be zero.
• No engine has ever been built for which this is true. Some heat is always rejected a cold reservoir.
• The 2nd law is true for practical experiences.

Reversibility and Heat Engines

• Thermal efficiency of a heat Engine depends on degree of reversibility of its operation
• A heat engine operating in a completely reversible manner is very special and called a Carnot engine.
• The reversible cycle is as follows:
  • Step 1: A system at temperature Tc undergoes a reversible adiabatic process that causes its temperature to rise to that of a hot reservoir at TH.
  • Step 2: The system maintains contact with the hot reservoir at TH and undergoes a reversible isothermal process during which heat |QH| is absorbed from the hot reservoir.
  • Step 3: The system undergoes a reversible adiabatic process (in the opposite direction of step 1) that brings its temperature back to that of the cold reservoir at Tc.
  • Step 4: The system maintains contact with the reservoir at Tc and undergoes a reversible isothermal process (in the opposite direction of step 2) that returns it to its initial state with rejection of heat |QC| to the cold reservoir.
• A Carnot engine operates between two heat reservoirs such that all heat absorbed is absorbed at constant temperature of hot reservoir & all heat rejected is rejected at constant temperature of cold reservoir.
• Any reversible engine operating between two heat reservoirs is a Carnot engine.

Carnot's Theorem

• For two given heat reservoirs, no engine can have a thermal efficiency higher than that of a Carnot engine.
• AB = Reversible isothermal heat absorption.
• BC = Reversible adiabatic expansion.
• CD = Reversible isothermal heat rejection.
• DA = Reversible adiabatic compression.
• AB - Heat is transferred reversibly and isothermally to the working substance from hot reservoir at temp TH.
• BC - During reversible adiabatic expansion (BC) temperature of a system decreases from TH to TC. [W = work done].
• CD - During the process, the system rejects heats QC to cold reservoir at constant temperature TC.
• DA - During which temperature rises from TC to TH & original conditions are restored reverse adiabatic Compression.

Carnot Refrigerators

• Assume that an engine E has a thermal efficiency greater than that of a Carnot engine.
• C - Engine absorbs heat from a hot reservoir and produces a constant work and reject heat to a cold reservoir.
• If engine E has a greater efficiency then |W| > |W' | and |QH| > |QH' |
• Let the engine E then drive the Carnot engine backward as a Carnot refrigerator, the net heat extracted from the cold reservoir is calculated as follows.
• Then the sole result of combining them is the heat transfer from the higher temperature to lower temperature without aid of the agency.

Carnot Violation of statement 2

• Violation of statement 2: No process is possible that consists solely in the transfer of heat from one temp level to a higher one.
• In similar function it can be prove that not all carnot engine operating between equal heat reservoir at the same two temperature have the thermal efficiency.
• corollary to carnot's theorem: The thermal efficiency of a carnot engine depends only on the temp. levels of not upon the working substance of the engine.
• Thermodynamic Temp. Scales :- [Y.V.C. Rao] tells us that efficiency of a reversible engine operating on both two given thermal reservoirs does not depend on nature of working medium but depends only on temp. of the reservoirs.
• fact can be made use of in establishing a temp. scale which is independent of working medium of thermometric property of substance.
• The temp. scale. The establishment of a temp scale follows from second law of thermodynamics as consequence.
• Therefore with 01,02,03 being at temperature 1,2,3 a carnot function is able to represent absorbed function from three reservoir and the relation is only dependent on temperature.
• The nature of the function F can be given $(01, 02) = $(01,) 4(02) then $2/1=(1/2/1) then the choice for function is set to $(0)=T.
• 191|/|12| = To/Te
• Hence ideal gas. temp scale & thermodynamic temp. scale is equivalent if a value of  273.16 K is assigned to triple point of water.
• Thermal efficiency is a concept related to Heat engine. Can be called as. Energy conversion Efficiency.
• But the heat Pump or refrigerator is not an energy conversion device so its performance is expressed in Coefficient of Performance (cop).
• COP = Energy effect sought / Energy consumed to accomplish task.
• (COP)R = 1QL1 /W = |QL| /(|QH| - |QL|) = TL/(TH - TL)
• (COP)HP = |QH| /W = |QH| /(|QH| - |QL|) = TH/(TH - TL)

Entropy

• The second law of thermodynamics states that all spontaneous processes are to some extent re-reversible and are accompanied by a degradation of energy.
• To make these statements quantitative there is required some function that always changes in a certain way during a spontaneous process of therefore, will characterize such a change
• Entropy is fundamental in the development of the second law.
• If air at 1.5 bar and 300K are separated into Oxygen and Nitrogen, it is possible by the first law.
• Increase in entropy is possible. Entropy is thermodynamic property.

Entropy and Heat

• Entropy is a measure of the unavailability of energy.
• Among the variable forms, heat is heat is the least available form of energy.
• Consideration of 1kg of water at the top and how the original irreversible process results in entropy change of fluid.

Increasing Entropy:

• Increase in case that entropy results from addition of heat in to system through the degradation of energy in heat.
• Heat exchanged can be used to show increase with entropy.

Entropy & temperature

• Amount of Heat added to a system is only a partial measure of the magnitude of its entropy increase
• It also depends upon the temp of system to which heat is added. .as transfer of energy to a low temp. leads to grader degradation than that resulted by transferrred energy.
• Also related to possible degradation where entropy is measured.

Mathematical statement of second Law:

Consider two hear reservoir, one is Temp TH & a second point at tempt Tc. let. quantity as a form of heat in the transfer of hear Total entropy is as Astotal = Astn * Asta, and Ast is positive in heat.