All Laws of thermodynamics explained in detail. Zeroth Law of Thermodynamics, First Law of Thermodynamics, Second Law of Thermodynamics, Third Law of Thermodynamics
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Zeroth Law of Thermodynamics
Suppose there are three bodies, Body "A," Body "B," and Body "C."
Body "A" is in equilibrium with Body "B," and Body "B" is in equilibrium with Body "C." So we can say Body "A" is also in equilibrium with Body "C." As shown in the figure below.
Zeroth law is very important in making the thermometer, or we can say that thermometer is working on the principle of zeroth law.
First Law of Thermodynamics
- Whenever a quantity of one form of energy is produced, an exactly equal amount of another kind of energy must be used.
- "Energy of the universe is conserved."
- The first law of thermodynamics is also known as Law of conservation of energy
- For a system undergoing a cycle of changes, the algebraic summation of all work effects exactly equals the summation of all heat effects.
- Q – Heat added to the system.
- Q is positive when heat is added to the system and,
- Q is negative when heat is rejected from the system.
- W – Work done by the system
- W is positive when work is done by the system and,
- W is negative when work is done on the system.
- If Heat and Work both are measured in the same units, \[\boxed{\sum W = \sum Q} \]
- From the statement of the first law of thermodynamics, the total energy change within the system equals the heat transferred into the system minus the work done by the system. \[\Delta E_{sys}= \Delta KE + \Delta PE + \Delta U = Q- W\]
- For an isolated system, \[dQ = 0, dW = 0\]
- Consider an idealized flow system as shown in the figure below.
- Fluid is flowing through the apparatus from section 1 to section 2. \(Velocity = u\),
- Heat Q is added per unit mass of the fluid through the heat exchanger and shaft work \(W_S\) is extracted through a turbine or any other suitable device.
Energy can nighter be created nor be destroyed, it can only convert from one form of energy to another form of energy.
The first law of Thermodynamics for a cyclic process
The first law of thermodynamics for a closed system
Where,
\(\Delta E_{sys} =\) The total energy change within the system,
\(\Delta KE =\)Change in Kinetic Energy,
\(\Delta PE = \) Change in Potential Energy,
\(\Delta U = \)Change in Internal Energy,
\(Q = \) Heat,
\(W = \) Work.
For a steady-state non-flow process in which there are no changes in the KE and PE, the above equation simplifies to
\[\boxed{\Delta U = Q - W}\]For differential changes in the thermodynamic state of a closed system,
\[\boxed{dU = dQ - dW}\]Thus,
\[dU = 0\]The first law of Thermodynamics for flow processes or open systems
\(Specific \; Volume = V\),
\(Pressure = P\),
\(Height \; above \; the \; datum \; level = Z\),
\(Internal \; Energy = U\),
\(Mass \; of \; the \; fluid = m\),
\(Suffix \; 1 = Conditions \; at \; sections \; 1\),
\(Suffix \; 2 = Conditions \; at \; sections \; 2\)
Internal energy of incoming fluid = \(mU_1\)
Internal energy of outgoing fluid = \(mU_2\)
Potential energy of fluid at inlet = \(mgZ_1\)
Potential energy of fluid at outlet = \(mgZ_2\)
Kinetic energy of incoming fluid = \(\frac{1}{2} mu_1^2\)
Kinetic energy of outgoing fluid = \(\frac{1}{2} mu_2^2\)
Flow energy required to push in liquid at inlet = \(mP_1V_1\)
Flow energy required to push out liquid at outlet = \(mP_2V_2\)
Total energy at section 1 = \(mU_1 + mgZ_1 + \frac{1}{2} mu_1^2 + mP_1V_1\)
Total energy at section 2 = \(mU_2 + mgZ_2 + \frac{1}{2} mu_2^2 + mP_2V_2\)
Net energy imparted to the fluid = \(mQ – mW_S\)
For unit mass of fluid, energy balance gives,
\[U_1 + gZ_1 + \frac{1}{2} + u_1^2 + P_1V_1 + Q - W_S = U_2 + gZ_2 + \frac{1}{2}u_2^2 + P_2V_2\] \[\Delta U + \Delta (PV) + g \Delta Z + \frac{1}{2} \Delta u^2 = Q + W_S\] \[\Delta H + g \Delta Z + \frac{1}{2} \Delta u^2 = Q - W_S\]For most applications in thermodynamics, the KE and PE terms are negligible with compared to the other terms. Thus the first law of thermodynamics for flow processes reduces to
\[\boxed{\Delta H = Q - W_S}\]Limitation of First Law of Thermodynamics
- The first law of thermodynamics can not tell about the direction of the process.
- It can not tell us about equilibrium conditions.
- It can not give a qualitative difference between Heat and Work.
Second Law of Thermodynamics
Various Statements of Second Law of Thermodynamics.
- Kelvin-Planck Statement
- Clausius Statement
Heat cannot pass by itself from a cold body to a hot body.
All spontaneous processes are, to some extent, irreversible and are accompanied by a degradation of energy.
Every system, when left to itself, will on an average, change toward a system of maximum probability.
It is impossible to construct an engine that, operating continuously (in a cycle), will produce no effect other than the transfer of heat from a single thermal reservoir at a uniform temperature and the performance of an equal amount of work.
This statement can also be stated in the following way.
No apparatus can operate in such a way that its only effect (in system and surroundings) is to convert heat absorbed by a system completely into work done by the system.
It is impossible to construct a heat pump that, operating continuously (in a cycle), will produce no effect other than the transfer of heat from a lower temperature body to a higher temperature one.
This statement can also be stated in the following way.
No process is possible which consists solely in the transfer of heat from one temperature level to a higher one.
It is impossible by a cyclic process to convert the heat absorbed by a system completely into work done by the system.
The mathematical statement of the second law of thermodynamics.
- Consider the adiabatic closed system.
- Path \(AB\) shows irreversible adiabatic operation.
- Curve \(AB\) is the pressure-volume relationship of the irreversible process (spontaneous process) occurring in a closed adiabatic (no heat interaction between system and surroundings) system.
- Work done by the system in this process is \(W_{AB}.\)
- Let system brought back to its original state by reversible path \(BA.\)
- In this cyclic process, the overall energy and entropy changes must be zero.
- So the change in internal energy \(\Delta U\) must be zero.
- From the first law of thermodynamics, we can say that net heat interaction must be equal to net work interaction. \[Q_{BA}=W_{AB}+W_{BA}\]
- If \(Q_{BA}\) is Positive, which means the system receives heat and converts completely into work. Which is a violation of the second law of thermodynamics.
- So the \(Q_{BA}\) is either Zero or Negative.
- \(Q_{BA} = 0\) is not possible, because it represents a reversible cyclic process, but then here we considered it irreversible.
- So, \(Q_{BA}\) is negative and the entropy change \(\Delta S_{BA}\) for reversible change can be calculated by \(Q_{BA}/T\) is also negative. \[\Delta S < 0\]
- Therefore entropy change for the path \(AB\) must be positive. Because entropy change for the cycle as a whole is zero. \[\Delta S > 0\]
- So, we can conclude that the entropy change of an isolated system (adiabatic closed system) in any process must be greater than or equal to zero. \[\boxed{\Delta S_{Isolated System} \geq 0}\]
- In nature, an Isolated system is made of a combination of system and surroundings.
- So, we can write, \[(\Delta S)_{Syatem}+(\Delta S)_{Surroundings} \geq 0\]
- Therefore we can conclude that the spontaneous process occurring in a closed adiabatic system is accompanied by an increase in entropy.
- From the value of entropy change, we can determine the direction of change.
- Process for which entropy change is Positive, Process is possible.
- Process for which entropy change is Negative, Process is not possible.
- Validity of the above equations can be verified for the process in which an amount of heat \(Q\) is transferred from a heat source at temperature \(T_1\) to a heat sink at temperature \(T_2.\)
- Entropy change of Heat Source \(= -Q/T_1.\)
- Entropy change of Heat Sink \(= Q/T_2.\)
- The total entropy change of heat source and sink is given by \[(\Delta S)_{Total}= \frac{-Q}{T_1}+\frac{Q}{T_2}=Q \frac{T_1-T_2}{T_1T_2}\]
- If \(Q\) is positive and the heat transfer is carried out irreversibly, when there exists a finite difference in the temperature of heat source and heat sink, \((\Delta S)_{total}\) would be positive.
- The process can be made reversible by lowering the temperature \(T_1\) to a value only slightly greater than \(T_2.\)
- Here, in this case, the \((\Delta S)_{Total}\) approaches zero, and for a true reversible process, the value becomes equal to zero.
- So, \[\boxed{(\Delta S)_{Total} \geq 0}\]
- The above equation is also known as the principle of increase in entropy
- From the principle of increase in entropy, spontaneous processes that occur in the isolated system are those processes that have increased in entropy.
- The universe is the perfect example of an isolated system, so all naturally occurring processes increase the entropy.
- Therefore we can say that the entropy of the universe goes on increasing.
It is the general mathematical statement of the second law of thermodynamics.
It is also referred to as the general mathematical statement of the second law of thermodynamics.
Combine statement of first and second law of thermodynamics is:- "The energy of the universe is conserved but the entropy of the unerverse is keeps on increasing."
Third Law of Thermodynamics
- Entropy is the reference property and is absolute like pressure, volume, and temperature.
- The third law of thermodynamics can be useful to calculate the absolute value of entropy.
- Assign zero value of the entropy to perfect crystalline substance at absolute zero temperature.
- Let substance be in the vapor phase at \(T\) temperature.
- Measure the heat capacity at different temperatures and the latent heat of phase change from absolute zero temperature to \(T\) temperature.
- Let melting point of the substance is \(T_f,\) and boiling point of the substance is \(T_b.\)
- The entropy at temperature \(T\) can be calculated as follows, \[S = \int_{0}^{T_f}\frac{C_{PS}dT}{T}+\frac{\Delta H_f}{T_f}+\int_{T_f}^{T_b}\frac{C_{PL}dT}{T}+\frac{\Delta H_V}{T_b}+ \int_{T_b}^{T}\frac{C_{PG}dT}{T}\] Where,
The absolute entropy is zero for all perfect crystalline substances at absolute zero temperature.
\(C_{PS}=\)Specific heat of solid,
\(C_{PL}=\)Specific heat of liquid,
\(C_{PG}=\)Specific heat of gas,
\( \Delta H_f=\)Latent heat of fusion,
\( \Delta H_V=\)Latent heat of vaporisation
Thermodynamic Properties of Fluid
Helmholtz Free Energy and Gibbs Free Energy
Derivation of Maxwell's Equations
Important Unit Operations of Chemical Engineering
Fundamentals of Heat Transfer
Newtonian and Non-Newtonian Fluids
Hydrostatic Equilibrium