Thermal equilibrium and Zeroth law
* Thermodynamics is the study of “exchange of ‘heat’ and ‘work’ between a system and its surrounding “, and the “resultant changes in the macroscopic variables of the said system”.
* A thermodynamic system is an isolated body or a group of bodies with a well defined boundary.
* The state of a system changes:
1. If the system exchanges heat with its surroundings.
2. When ‘work’ is done by the system or on the system.
* An adiabatic wall does not allow any flow of heat through it where as diathermic wall allows flow of heat through it.
* Two systems ‘A’ and ‘B’ are said to be in “thermal equilibrium”, when they are in contact with each other or separated by a diathermic wall and the system A is in equilibrium with the state of system B.
* When two systems, ‘A’ and ‘B’ are individually in thermal equilibrium with a third system ‘C’, they are in thermal equilibrium with each other.
* This is known as “Zeroth law of Thermodynamics”.
Heat, internal energy and work
* Temperature is a thermodynamic variable that is equal for system in thermal equilibrium.
* Heat is energy in transit.
* The macroscopic thermodynamic variable of a system that changes when it either emits or absorbs heat energy is its internal energy.
* Internal energy=total kinetic energy of all molecules due to their translational, rotational and vibrational motions+ potential energy of the molecules associated with inter-molecular bonds.
* We have two different ways of changing the internal energy of a system: heat and work.
* Heat and work are two modes of energy transfer to a system.
* Heat and work are not state variables; they depend on the path through which the system is taken.
* The internal energy of a system depends only on its state and is independent of the path through which it is taken.
First law of thermodynamics
* There are two different ways to transfer energy to a system: heating and doing work.
* The relationship between the three important physical quantities- heat, internal energy and work is expressed by the First Law of Thermodynamics.
* The First law of Thermodynamics states that the change in the internal energy of a system is equal to the heat absorbed by the system minus the work done by it on the surroundings.
* First law of Thermodynamics: delta U is equal to delta Q minus delta W or delta Q is equal to delta U plus delta W.
* ‘First law of Thermodynamics’ is an expression of the “general principle of conservation of energy”.
* “Delta Q“ is positive if heat is absorbed by the system and negative if heat is given out by the system.
* “Delta W” is positive if work is done by the system and negative if work is done on the system.
* Work done by a system delta W is equal to P delta V.
*If a thermodynamic process is represented by a P-V graph, then the work done by the system is the area bound by the P-V curve and the V axis for the range of change in the volume of the system.
* CP minus CV is equal to R.
Thermodynamic state variables and equation of state
* The set of values of properties of a thermodynamic system that are used to reproduce the system is known as “thermodynamic state”, and the properties are also called “variables”.
* If the variables that describe state have uniform values throughout the system and they do not change with time, then the system is said to be in “equilibrium state”.
* Not every state of a system is in “equilibrium state”. Free expansion of gas is not an equilibrium state.
* If the pressure of the system is equal to the external pressure, then the system is said to be in “mechanical equilibrium”.
* If the temperature of the system is equal to the temperature of the surroundings then the system is said to be in thermal equilibrium with its surroundings.
* The variables that describe equilibrium state of a thermodynamic system are known as “thermodynamic state variables”.
* The state variables of a system depend only on the state of the system and they do not depend on the path through which the system is taken to attain this state.
* The relationship between state variables is called “equation of state”.
* For an ideal gas, equation of state is expressed as PV=µRT.
* The equation of state for a real gas is expressed by van der waals’ equation –[P + a/V2] (Vb) = µRT
* State variables are of two types – extensive state variables and intensive state variables.
* A state variable that depends on the size of the system is called an “extensive variable”.
* An “intensive variable” does not depend on the size of the system and has a uniform value in different subdivisions of the system.
* In an thermodynamic equation, quantities on both sides must be either “extensive” or “intensive”.
Thermodynamic processes
* A “quasi static process” is an idealized process in which the system is in an equilibrium state at every stage.
* In principle, a quasi static process is infinitely slow.
* If the temperature of a system is constant throughout a thermodynamic process, it is called an “isothermal process”.
* There will no change in the internal energy of an ideal gas in an isothermal process.
* For an ideal gas in an isothermal process,
* The first law of thermodynamics reduces to ∆Q=∆W.
* Work done by a system in an isothermal process is W=µRT ln V2/V1.
* The p-v graph of a system passing through a process at a fixed temperature is called an “isotherm”.
* If a system undergoes a process in which heat is neither extracted from it nor supplied to it, the process is called an “adiabatic process”.
* For an adiabatic process ∆Q= 0, THE First Law of Thermodynamic reduces to ∆U= -∆W
* Sometimes a system passes through a process very quickly so that there is not enough time for an exchange of heat with its surroundings. Such processes are also called adiabatic processes.
* W = (P2V2-P1V1)/(1-Y) or W= µR (T2 –T1)/(1-Y)
* If a thermodynamic process takes place at a constant pressure, it is called an “adiabatic process”.
* For an isothermal process, W= P(V2-V1).
* If the system is an ideal gas, then W=µR(T2-T1).
* In an isochoric process, the volume of the system remains constant.
* For an isochoric process, ∆V=0, Therefore, ∆W=P ∆V=0.
Heat engines and refrigerators
* A device that converts heat energy into mechanical energy is called a heat engine.
* In a heat engine, the working substance undergoes a sequence of processes that finally leave it in the same state in which it started. Such a process is called a cyclic process.
* In each cycle, the working substance passes through the following main processes.
• Absorbs heat from a hot reservoir
• Does some work on the surroundings
• Rejects some heat to a cold reservoir
* In a cyclic process, there is no change in the internal energy of the system. ∆U=0.
* The efficiency of a heat engine is defined as the ratio of the work done by the system to heat absorbed.
* The efficiency of a heat engine, ɳ= 1- Q2/Q1.
* It is not possible to construct a heat engine with 100 percent efficiency.
* There are two different types of heat engines.
• Internal combustion heat engines: diesel and petrol engines are examples of internal combustion engines.
• External combustion heat engines: a stream engine is an example of an external combustion engine.
* The four strokes of a petrol engine are:
• Intake stroke
• Compression stroke
• Power stroke
• Exhaust stroke
* A refrigerator is a device that takes heat from a cold reservoir, and after some external work is done on it, it releases some heat to a hot reservoir.
* The coefficient of performance, alpha, of a refrigerator is defined as the ratio of heat taken from the cold reservoir to the work done.
⍺=Q1/W.
Second Law of Thermodynamics
* The second law of thermodynamics is the principle of nature, which disallows certain processes from taking place even though they are consistent with the First Law of Thermodynamics.
* Second law of thermodynamics: Kelvin- Planck statement: No processes whose sole result is to absorb heat from a reservoir and convert it completely into work is possible.
* Second law of thermodynamics: Clausius Statement: No process is possible whose sole result in the transfer of heat from a colder object to a hotter object.
* The second law restricts the availability of energy and the ways in which it can be used and converted.
Reversible and irreversible processes
* A process is called a “reversible process” if the system and its surroundings can be brought back to their initial states without causing any change anywhere else in the universe.
* For a process to be reversible it must be quasi static and there must be no dissipative effects.
* A heat engine based on idealized reversible processes achieve the highest efficiency possible.
Carnot engine
* A reversible heat engine operating between two temperatures is called “Carnot Engine”.
* The cycle of two isothermal and two adiabatic processes through which the working substance of a Carnot engine passes is known as “Carnot Engine”.
* The efficiency of the Carnot Engine ɳ=1 – (T2/T1)
Carnot Theorem:
* Working between the same temperatures, no engine can have efficiency greater than that of the Carnot Engine. It also states that the efficiency of the Carnot Engine is independent of the nature of the working substance.
* Q2 by Q1 is equal to T2 byT1 is universal relation and is independent of the nature of the system.