# Second Law of Thermodynamics Study Notes for GATE & Mechanical Engineering Exams

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The Second Law of Thermodynamics tells us that processes occur in a certain direction and that quality is also attached to the quantity of the energy. As per the first law, there is no restriction on the direction of a process, and satisfying the first law does not guarantee the occurrence of that process. Hence, another principle (second law) to identify whether a process can occur or not is needed.

Here we are providing the complete study notes on the Second Law of Thermodynamics for the preparation of GATE, SSC JE, ISRO, ESE, and other mechanical engineering exams.

The second law of thermodynamics tells us that processes occur in a certain direction and that quality is also attached to the quantity of the energy. As per the first law, there is no restriction on the direction of a process, and satisfying the first law does not guarantee the occurrence of that process. Hence, another principle (second law) to identify whether a process can occur or not is needed.

The figure shown above shows us that the heat transfer process can occur only when it satisfies both the first and the second laws of thermodynamics.
• The second law also asserts that energy has a quality attached to it and its preservation is a major concern of engineers. In the above example, it can be seen that the energy contained in the hot container (present at a higher temperature) has a higher quality (ability to work) compared to the energy stored (at a lower temperature) in the surroundings.
• The second law is also used in the determination of the theoretical limits of the performance of the general engineering systems like heat engines and refrigerators etc.

## Thermal Energy Reservoirs

• Thermal energy reservoirs are hypothetical bodies that have a relatively large thermal energy capacity (mass × specific heat). They can supply or absorb infinite amounts of heat without undergoing any change in temperature.  Lakes, atmosphere, seas are examples of thermal reservoirs.
• As a two‐phase can absorb and release large quantities of heat while remaining at a constant temperature, therefore it can be modelled as a reservoir.
• A reservoir that supplying energy in the form of heat is called a source and the one absorbing energy in the form of heat is known as the sink.

## Heat Engines

• Heat engines perform the work of conversion of heat into work. The working of  heat engines is described as follows :
• receiving heat from a high‐temperature source (oil furnace, nuclear reactor, etc.)
• conversion of a part of this heat to work
• rejection of the remaining waste heat to a low‐temperature sink
• cyclic operation

• Thermal efficiency: Ratio of the Network generated to the total heat supplied to the engine.

• The thermal efficiencies of work‐developing systems are low. The thermal efficiency of ordinary spark‐ignition automobile engines is about 20%, the thermal efficiency of diesel engines is about 30%, and that of a power plant is in the range of 40%.

## The Second Law: Kelvin‐Planck Statement

• The Kelvin Planck statement is it is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work. In other words, its impossible for a heat engine to attain a thermal efficiency of 100%.

The figure above shows a heat engine that violates the Kelvin‐Planck statement of the second law and such a heat engine cannot be built.

## Refrigerators and Heat Pumps

• Naturally, heat flows from higher temperature regions to lower temperature ones. It is not possible for the reversal of this process to occur by itself.
• Special devices are used for the transfer of heat from a lower temperature region to a higher temperature one namely refrigerators and heat pumps.
• Refrigerators and heat pumps are cyclic devices where the working fluids used in the cycles are called refrigerants.
• Refrigerators and heat pumps are more or less the same devices; differing in their objectives only. A refrigerator maintains the refrigerated space at a lower temperature whereas a heat pump absorbs heat from a lower temperature source and supplies the heat to a warmer medium.

## Coefficient of Performance (COP)

• The performance of heat pumps and refrigerators is expressed in terms of the coefficient of performance (COP) which is expressed as:

• Mathematically, it can be seen that:
COPHP = COP+ 1
• Air conditioners perform nearly the same task refrigerators perform but the refrigerated space is a room or a building.
• The Energy Efficiency Rating (EER) is the ratio of the quantity of heat removed from the cooled space to the power consumed by the unit.
• Most air conditioners have an EER in the range of 8 to 12 (with COP of 2.3 to 3.5).

## The Second Law of Thermodynamics: Clausius Statement

• The Clausius statement is – It is impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a lower‐temperature body to a higher‐temperature body.
• A refrigerator can only operate when its compressor is driven by an external power source.
• Kelvin‐Planck and Clausius’s statements of the second law both being negative statements, cannot be proved.
• The two statements of the second law are equivalent and therefore any device violating the Kelvin‐Planck statement also violates the Clausius statement and vice versa.

The violation of the Kelvin‐Planck statement leads to the violation of the Clausius statement is being shown in the above figure.

Note:

• A perpetual‐motion machine of the first kind (PMM1) is a device that violates the first law of thermodynamics (by generating energy).
• A perpetual‐motion machine of the second kind (PMM2) is a device that violates the second law of Thermodynamics.

## Reversible and Irreversible Process

•  A reversible process is a process that can be reversed without causing any permanent change in the surroundings. That is, both the system and the surroundings return to their initial states if the given process is reversed. In the property diagrams, reversible processes are shown by continuous line or curve whereas irreversible processes are shown by dotted line or curve.

Reversible processes are actually only theoretical. They are a mere idealization of actual processes. Processes that are not reversible are termed irreversible processes.

• Some of the factors causing irreversibilities in a process are listed below:
• Friction
• Unrestrained expansion and compression
• mixing
• Heat transfer (finite ∆T)
• Inelastic deformation
• Chemical reactions

## Internally Reversible process

• In this, no irreversibilities are present within the boundaries of the system. In these processes, a system undergoes a series of equilibrium states and on reversing the process the system passes through exactly the same equilibrium states while returning to its initial state.

The Carnot Cycle

• The execution of the processes that make up a heat engine cycle greatly affects the efficiency of the cycle.
• The maximum efficiency could be attained if all the processes involved are made reversible and the best known reversible cycle is the Carnot cycle.
• Reversible cycles are practically not possible due to the irreversibilities involved.
• The reversible cycles give us an idea of the upper limits on the performance of real cycles.
• The Carnot cycle has four processes:
• 1‐2 Reversible isothermal expansion
• 3‐4: Reversible isothermal compression
• The thermal efficiency of a heat engine (reversible or irreversible) is provided by the following expression :
• For the Carnot cycle, it is:

Fig above shows a P‐v diagram for the Carnot cycle.

•  An irreversible (real) cycle operating between the same two thermal reservoirs has an efficiency that is always lesser than the Carnot cycle.

The Carnot Refrigeration and Heat Pump Cycle

• A refrigerator or heat pump operating on the reversed Carnot cycle is called a Carnot Refrigerator, or a Carnot heat pump.
• The COP (Coefficient of Performance) of any refrigerator or heat pump (reversible or irreversible) is given by:
• COP of all reversible refrigerators or heat pumps can be calculated by:

Also, similar to a heat engine, one can conclude:

This topic is important for GATE MEISRO MEESE IES ME, and other Mechanical exams.

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