THERMODYNAMICS
THERMAL EQUILIBRIUM
Two systems are said to be in thermal equilibrium with each other if they have the same temperature.
ZEROTH LAW OF THERMODYNAMICS
The zeroth law of thermodynamics is a fundamental principle that provides the foundation for the concept of temperature and temperature equilibrium. It states that if two systems are separately in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.
In simpler terms, the zeroth law asserts that if two objects are in thermal equilibrium with a third object, then they are also in thermal equilibrium with each other. This law is crucial because it allows us to define and compare temperatures objectively.
Temperature is a measure of the average kinetic energy of the particles in a system. When two systems are in thermal equilibrium, there is no net flow of heat between them, meaning their temperatures are equal. By establishing this equality of temperature, the zeroth law allows for the creation of temperature scales and the development of thermometry.
If objects A and B are separately in thermal equilibrium with a third object C then objects A and B are in thermal equilibrium with each other.
ABOUT FIRST LAW OF THERMODYNAMICS
First law of thermodynamics gives a relationship between heat, work and internal energy.
HEAT
It is the energy which is transferred from a system to surrounding or vice-versa due to temperature difference between system and surroundings.
It is a macroscopic quantity.
It is path dependent i.e., it is not a point function.
If the system liberates heat, then by sign convention it is taken negative, If the system absorbs heat, it is positive.
WORK
It is the energy that is transmitted from one system to another by a force moving its points of application. The expression of work done on a gas or by a gas is
where V1 is volume of gas in initial state and V2 in final state.
It is also a macroscopic and path dependent function.
By sign convention it is positive if the system does work (i.e., expands against surrounding) and it is negative, if work is done on system (i.e., contracts).
In a cyclic process the work done is equal to area under the cycle and is negative if cycle is anti-clockwise and positive if cycle is clockwise (shown in fig.(a) and (b)).
INTERNAL ENERGY
The internal energy of a gas is the sum of internal energy due to molecular motion (called internal kinetic energy UK) and internal energy due to molecular configuration (called internal potential energy UP.E.)
i.e., U = UK + UP.E. ……(1)
In ideal gas, as there is no intermolecular attraction, hence
……(2)
(for n mole of ideal gas)
Internal energy is path independent i.e., point function.
In the cyclic process, there is no change in internal energy (shown in fig.)
i.e., dU =Uf – Ui = 0
⇒ Uf = Ui
Internal energy of an ideal gas depends only on temperature eq.(2).
First law of thermodynamics is a generalisation of the law of conservation of energy that includes possible change in internal energy.
FIRST LAW OF THERMODYNAMICS
The first law of thermodynamics, often referred to as the law of energy conservation, states that energy cannot be created or destroyed within an isolated system. It can only be converted from one form to another or transferred between different parts of the system.
In simple terms, the first law asserts that the total energy of a closed system remains constant over time. It emphasises the principle of energy conservation, highlighting that energy is a fundamental quantity that is conserved throughout various thermodynamic processes.
This law has significant implications for understanding and analysing energy transfers and transformations. It forms the basis of energy balance equations, which are used to describe the flow of energy into and out of a system, as well as the changes in its internal energy.
The first law of thermodynamics is a fundamental principle that asserts the conservation of energy within an isolated system. If a certain quantity of heat dQ is added to a system, a part of it is used in increasing the internal energy by dU and a part is used in performing external work done dW.
i.e.,
The quantity dU (i.e., dQ – dW) is path independent but dQ and dW individually are not path independent.
APPLICATIONS OF FIRST LAW OF THERMODYNAMICS
In isobaric process P is constant
so
so dQ = dU + dW = n CP dT
In cyclic processes heat given to the system is equal to work done (area of cycle).
In isothermal process temperature T is constant and work done is
Since, T = constant so for ideal gas dU = 0
Hence, (for ideal gas)
In isochoric process W = 0 as V = constant
It means that heat given to the system is used in increasing internal energy of the gas.
In adiabatic process heat given or taken by system from surrounding is zero
i.e., dQ = 0
It means that if the system expands dW is +ive and dU is –ive (i.e., temperature decreases) and if the system contracts dW is –ive and dU is +ive (i.e., temperature increases).
THERMODYNAMIC PROCESSES Thermodynamic processes are fundamental concepts in the study of thermodynamics that describe how energy is transformed within a system. These processes involve the transfer and conversion of energy from one form to another, allowing us to understand and analyse the behaviour of various systems.
A thermodynamic process typically involves a change in one or more thermodynamic variables, such as temperature, pressure, volume, or internal energy. By studying these variables and their interactions, we can gain insights into the behaviour and characteristics of systems undergoing specific processes.
Different types of thermodynamic processes include isothermal, adiabatic, isobaric, and isochoric processes, among others. Each process has distinct characteristics and relationships between the thermodynamic variables involved.
TYPES OF THERMODYNAMIC PROCESSES
ISOTHERMAL PROCESS
Isothermal Process: Maintaining Constant Temperature
An isothermal process is a thermodynamic process in which the temperature of a system remains constant throughout the entire process. It is characterised by a careful balance of heat transfer to or from the system to maintain a steady temperature.
During an isothermal process, the energy transferred into or out of the system compensates for any changes in internal energy, keeping the temperature constant. This is achieved by having the system in thermal contact with a heat reservoir or by carefully controlling the heat transfer to maintain equilibrium.
An isothermal process typically occurs at a slow and controlled rate to ensure that the system remains at a constant temperature.
An isothermal process is characterised by the maintenance of a constant temperature within a system.
If a thermodynamic system is perfectly conducting to surroundings and undergoes a physical change in such a way that temperature remains constant throughout, then the process is said to be an isothermal process.
For isothermal process, the equation of state is
PV = nRT = constant, where n is no. of moles.
For ideal gas, since internal energy depends only on temperature.
or
ADIABATIC PROCESS
Adiabatic Process: Energy Transfer through Insulation
An adiabatic process is a thermodynamic process in which there is no heat transfer into or out of a system. It occurs when a system is well-insulated, preventing any exchange of heat with its surroundings.
During an adiabatic process, the system undergoes changes in its internal energy without any heat transfer. This means that any changes in temperature, pressure, volume, or other thermodynamic variables are solely the result of work done on or by the system.
Adiabatic processes are typically characterised by rapid and efficient energy transfers. The absence of heat exchange allows the system to focus solely on the conversion of energy through work, resulting in changes in temperature or pressure.
For example, the compression and expansion of gases in a piston-cylinder arrangement or the rapid expansion of a fluid in a turbine are adiabatic processes.
An adiabatic process occurs when a system experiences no heat transfer with its surroundings. It focuses on energy transfer through work alone, allowing for rapid and efficient energy conversions.
If a system is completely isolated from the surroundings so that no heat flows in or out of it, then any change that the system undergoes is called an adiabatic process.
For ideal gas, dQ = 0
dU = μCVdT (for any process)
(where PVγ = K = constant)
where PVγ = constant is applicable only in adiabatic processes. Adiabatic process is called an isentropic process (in this process entropy is constant).
ISOBARIC PROCESS
Isobaric Process: Constant Pressure Transformation
An isobaric process is a thermodynamic process in which the pressure of a system remains constant throughout the process. It involves a careful balance of energy transfer and work done to maintain a steady pressure within the system.
During an isobaric process, the system may undergo changes in other thermodynamic variables, such as temperature or volume, while the pressure remains constant. The energy transferred into or out of the system compensates for these changes, allowing the pressure to remain steady.
Isobaric processes are often encountered in practical situations where the system is in contact with a constant-pressure environment or when external pressure is maintained.
For example, heating or cooling a substance in an open container under atmospheric pressure can be considered an isobaric process.
An isobaric process is characterised by the maintenance of a constant pressure within a system. It plays a significant role in understanding energy transfer, work done, and the behaviour of systems under constant pressure conditions.
A process taking place at constant pressure is called an isobaric process.
In this process
dQ = n CpdT, dU = n CVdT and dW = P(V2–V1)
ISOCHORIC PROCESS
Isochoric Process: Constant Volume Transformation
An isochoric process, also known as an isovolumetric or constant volume process, is a thermodynamic process in which the volume of a system remains constant throughout the process. It occurs when the system is confined and unable to change its volume.
During an isochoric process, no work is done by or on the system through volume change since the volume remains constant. However, energy transfer in the form of heat can still occur, leading to changes in other thermodynamic variables such as pressure and temperature.
Isochoric processes are commonly encountered in various practical scenarios, such as heating or cooling a substance in a closed, rigid container.
For example, the heating of a gas inside a fixed-volume cylinder without allowing it to expand or contract represents an isochoric process.
An isochoric process is characterised by the maintenance of a constant volume within a system. It plays a significant role in understanding heat transfer, pressure changes, and the behaviour of systems under constant volume conditions.
A process taking place at constant volume is called an isochoric process.
In this process, dQ = dU =n CVdT and dW = 0
CYCLIC PROCESS
In this process the initial state and final state after traversing a cycle (shown in fig.) are the same.
In cyclic process, dU = 0 = Uf – Ui and dW = area enclosed by the cycle = area (abcd)
Slope of adiabatic and isothermal curve
For isothermal process PV = constant
On differentiating, we get PdV + VdP = 0
And slope of isothermal curves
... (1)
For adiabatic process PVγ = constant
On differentiation, we get slope of adiabatic curve
.... (2)
It is clear from equation (1) and (2) that the slope of adiabatic curve is more steeper than isothermal curve as shown by fig by γ time (γ = CP/CV)
GRAPHS OF THERMODYNAMIC PROCESSES
In the figure (i) P–V graph the process ab is isothermal, bc is isobaric and ca is isochoric.
The fig (ii) is the P–T diagram of fig (i)
Figure below shows P–V diagrams for two processes.
The heat absorbed in process I is more than that in II. Because, area under process I is also more than area under process II. The work done in process I is more than that in II. Also, the change in internal energy is the same in both cases.
The P–V and corresponding V–T diagram for a cyclic process abca on a sample of constant mass of ideal gas are shown below:
For isochoric process, the P–V, V–T and P–T graphs :
For isobaric process, the P – V, P – T and V – T graphs :
For isothermal process, the P – V, V – T and P – T graphs :
POINTS TO REMEMBER
In thermodynamics heat and work are not state variables, whereas internal energy is a state variable.
For ideal-gas
relation between P and V is PVγ = constant
relation between V and T is TV γ–1 = constant
relation between P and T is TγP1–γ = constant
A quasi-static process is an infinitely slow process such that the system remains in thermal and mechanical equilibrium with the surroundings throughout.
Pressure, volume, temperature and mass are state variables. Heat and work are not state variables.
A graphical representation of the state of a system with the help of two thermodynamic variables is called an indicator diagram.
REVERSIBLE AND IRREVERSIBLE PROCESS
REVERSIBLE PROCESS
A process which can proceed in the opposite direction in such a way that the system passes through the same states as in the direct process and finally the system and the surroundings acquire the initial conditions.
CONDITIONS FOR A PROCESS TO BE REVERSIBLE
The process must be extremely slow.
There should be no loss of energy due to conduction, or radiation. The dissipating forces should not be in the system.
The system must always be in thermal and chemical equilibrium with the surroundings.
Examples : Fusion of ice, vaporisation of water, etc.
IRREVERSIBLE PROCESS
The process which cannot be traced back in the opposite direction is defined as an irreversible process.
Examples : Work done against friction, magnetic hysteresis.
In nature all processes are irreversible, because no natural process can fulfil the requirement of a reversible process.
HEAT ENGINE
A heat engine is a device which converts heat energy into mechanical energy.
Efficiency of heat engine is given by
where Q2 = amount of heat rejected per cycle to the sink (of temp T2)
Q1 = amount of heat energy absorbed per cycle from the source (of temp T1).
The efficiency of a heat engine η is never greater than unity, η =1 only for an ideal engine & for a practical heat engine η < 1.
REFRIGERATOR AND HEAT PUMP
Refrigerator or heat pump is a heat engine running in backward direction i.e. a working substance (a gas) takes heat from a cold body and gives it out to a hotter body with the use of external energy i.e. electrical energy. A heat pump is the same as a refrigerator.
The coefficient of performance of refrigerator or heat pump is
where T2 is the temperature of the cold body and T1 is the temperature of the hot body.
CARNOT ENGINE
Carnot devised an ideal engine which is based on a reversible cycle of four operations in succession : isothermal expansion, adiabatic expansion, isothermal compression and adiabatic compression.
Efficiency of Carnot engine,
=
The points B and C are connected by an adiabatic path as are the points D and A. Hence, using this equation and the adiabatic gas equation.
T1V2(γ – 1) = T2 V3(γ – 1) and T1V1(γ – 1) = T2 V4(γ – 1).
Combination of the above equations gives , and,
=
or,
The percentage efficiency of Carnot’s engine,
or
The efficiency of a Carnot engine is never 100% because it is 100% only if temperature of sink T2 = 0 which is impossible.
In a Carnot cycle,
or
CARNOT THEOREM
No irreversible engine (I) can have efficiency greater than Carnot reversible engine (R) working between the same hot and cold reservoirs.
i.e.,
or
SECOND LAW OF THERMODYNAMICS
Second Law of Thermodynamics:
Entropy and Irreversible Processes
The second law of thermodynamics is a fundamental principle in physics that deals with the concept of entropy and the directionality of natural processes.
It states that in any natural or spontaneous process, the entropy of an isolated system tends to increase over time.
Entropy can be understood as a measure of the disorder or randomness within a system.
The second law of thermodynamics asserts that the total entropy of a system and its surroundings will either remain constant in reversible processes or increase in irreversible processes.
This law implies that certain processes, such as the conversion of heat into work, are irreversible and result in an overall increase in entropy.
It introduces the concept of heat transfer occurring only from hot to cold objects, as heat flow from a colder object to a hotter object would violate the law by decreasing entropy.
The second law of thermodynamics has important implications for various fields, including engineering, chemistry, and biology. It helps to explain phenomena such as the efficiency limits of heat engines, the direction of chemical reactions, and the irreversibility of natural processes.
One of the key consequences of the second law is the concept of entropy production, which is the measure of how much entropy is generated within a system during a process.
The second law of thermodynamics states that the entropy of an isolated system tends to increase over time in natural processes.
It highlights the irreversibility of certain processes and the tendency of systems to move toward greater disorder.
It states that it is impossible for a self acting machine unaided by any external agency, to transfer heat from a body at a lower temperature to a body at higher temperature.
It is deduced from this law that the efficiency of any heat engine can never be 100%.
ENTROPY
Entropy is a measure of disorder of the molecular motion of a system. The greater the disorder, the greater is the entropy. The change in entropy is given by
(here T is not differentiable)
Clausius inequality
or,
or, dQ = TdS ≥ dU + PdV
Also, S = K logeω
is the microscopic form of entropy, where K is Boltzmann's constant and ω represents the number of possible microscopic states.
Energy entering a body increases disorder
Energy leaving a body decreases disorder
When a hot body is brought into thermal contact with a cold body for a short time, then :
Each body will experience a change in the entropy of its particle.
The hot body experiences a decrease in entropy (a negative change) of magnitude
The cold body experiences an increase in entropy (a positive change) of magnitude
The net change in entropy
The effect of naturally occurring processes is always to increase the total entropy (or disorder) of the universe.
