Laws of Thermodynamics and Energy Efficiencies

Laws of Thermodynamics and Energy Efficiencies

Law of conservation of energy states that the energy can neither be created nor destroyed. The total energy of the system is always conserved. However, the energy can change from one form of energy to another form of energy.

The extension of law of conservation of energy is the first law of thermodynamics. In engineering applications we are concerned with the conversion of heat into work or vice-versa either during the cycle or in a process.

1) 1^st Law of Thermodynamics as Applied to Cyclic Processes :

It states that if a closed system is taken through a cycle of processes, the algebraic sum of total energy transfers as heat and work will be zero. Mathematically,

φ (d’Q – d’W) = 0 …(1)

2) 1^st Law of Thermodynamics as Applied to Closed System Processes :

When a system executes a process, the net heat transfer equals to the algebraic sum net work transfer and the change in total energy of the system. Accordingly,

d’Q = d’W + DE  ….(2)

d’Q – d’W = dE ….(2.1)

Where, E represents the total energy of the system. or,

E is the property of the system. It includes the internal enerey, kinetic energy, potential energy, electrical energy. chemical energy etc. 

If a system is subjected to a process between state 1 to state 2, the first law equatice becomes : 

Q – W = E₂ – E1  ….(3)

(a) First law as applied to an isolated system : 

For an isolated system, both heat and work transfers across the boundary are zero. Thus from Equation (3.1.2) we can write, 

dE = 0 i.e. E Constant … (4) 

Above Equation (4) shows that the total energy of an isolated system is consened from its surroundings . Thus , it also refers to the law of conservation of energy. The total energy E of a closed system can be written in absence of other forms of energy, as 

E = Internal energy, U + Kinetic energy, 1/2 mc²+ Potential energy, mgz …. (5) 

The internal energy. U is the sum of thermal energy (as function of temperature) and chemical energy. Usually the changes in potential and kinetic energy of a closed system are negligible. 

Note that in above equation other forms of energy like electrical energy, biomass energy, magnetic energy etc. have be neglected.

3) First Law Efficiency : 

The ratio of output energy to the input energy to a device is defined as first Law efficiency. Therefore,

1^st law efficiency = Output energy / Input energy

4) Second Law of Thermodynamics :

First law of thermodynamics deals with the quantity of energy without differentiating between various forms of energy based on the law cl conservation of energy. According to this heat and work energies are equivalent. 

Whereas, the second law of thermodynamics states that the various forms of energy differ in quality. It shows that the spontaneous processes in nature are unidirectional i.e. they occur only in one direction. For example, heat always flows from a body at higher temperature to a body at lower temperature (Claustus statement). 

Similarly, it has been demonstrated by Joule’s experiment that the work energy can be completely converted into heat energy but the complete conversion of heat energy into work in a cyclic process is not possible (Kelvin-Plank statement. Thus the concept of quality of energy came into existence and work is considered high grade of energy and heat as low grade energy. The high grade form of work energy are electrical energy, wind energy, tidal energy etc, and low grade form of energy are chemical energy of fuels, heat from nuclear reactions.

We conclude from above that the complete conversion of low grade energy into high grade energy in a cycle is impossible. 

Following statements are derived from second law of thermodynamics : 

1. Spontaneous conversion of energy are irreversible.
2. Various forms of energy are not identical. They differ in quality. Work is a high grade form of energy and heat is a low grade form of energy.
3. Energy flow is unidirectional. It can only flow from higher potential to lower potential.
4. In energy conversion from heat to work, some amount of heat is rejected to the surroundings which increases the internal energy of the environment. This internal energy of the environment is worthless since this energy is not available for utilization practically.

5) Second Law Efficiency or Effectiveness of the System : 

First law efficiency was defined as the ratio of output energy to the input energy of a device. 1^st law is concerned only with quantities of energy without discriminating between the various forms of energies. It is the second law of thermodynamics which assigns an index to the quality of energy.

The availability of the system relates to the maximum useful work that can be obtained from a system. It is defined as the maximum useful work that can be obtained from the system during a process from its initial state to a dead state (when the system is in thermodynamic equilibrium with its surroundings) under ideal conditions (i.e. without dissipative effects). The minimum energy that has to be rejected to the sink (surroundings) is called the unavailable energy (U.E.) or energy. 

Therefore, the concept of available energy or energy provides a measure of energy quality. This concept of availability provides the means of minimizing the consumption of available energy to perform a given process in the most efficient manner.

The second law efficiency ηn or effectiveness of the system in a process is defined as the ratio of availability output to the availability input i.e. 

η_n = Availability output Availability input ….(7) 

But,

Availability in = Availability output + Availability loss + Availability destruction due to irreversibility 

η_n = Availability loss + Availability destruction due to irreversibility / Availability in ….(8)

Irreversibilty, I = Maximum useful work, W– Actual work, W_max

Therefore, second law efficiency (for power producing device) can be written as : and

 η_II = Actual work output, W / W_max   ….(9)

First law efficiency, 

η₁ = Actual work, W/ Heat supplied, Q_in 

_∴ η_I = W/Q_i = W/W_max x W_max / Q_i 

η_I =  η_II x  η_carrot

∴ η_II = η_I / η_carrot   ….(10)

But, η_carrot = Q_i (1 –  T₀/T)   ….(11)

Where, T₀ and T are the temperature of the surrounding and the system respectively.

I^st and II^nd law efficiecnices of solar collector :

Let,  Q_r = Solar energy available at reservoir storage temperature at temperature T_r

_{Qc = Energy transferred to solar collector at temperature} T_c

_{ηI = Qc}/ Q_r

_ηII = Availability output / Availability input

= Q_c (1 -T₀/T_c) / Q_r (1 -T₀/T_r)