Law of Thermodynamics

The 1st Law of Thermodynamics tells us that energy is neither created nor destroyed, thus the energy of the universe is a constant. However, energy can certainly be transferred from one part of the universe to another. To work out thermodynamic problems we will need to isolate a certain portion of the universe, the system, from the remainder of the universe, the surroundings.
The energy transfer between different systems can be expressed as:

E₁ = E₂         (1)
where
E₁ = initial energy
E₂ = final energy

The internal energy encompasses:

• The kinetic energy associated with the motions of the atoms
• The potential energy stored in the chemical bonds of the molecules
• The gravitational energy of the system

The first law is the starting point for the science of thermodynamics and for engineering analysis.
Based on the types of exchange that can take place we will define three types of systems:

• isolated systems: no exchange of matter or energy
• closed systems: no exchange of matter but some exchange of energy
• open systems: exchange of both matter and energy

The first law makes use of the key concepts of internal energy, heat, and system work. It is used extensively in the discussion of heat engines.

Internal Energy - Internal energy is defined as the energy associated with the random, disordered motion of molecules. It is separated in scale from the macroscopic ordered energy associated with moving objects; it refers to the invisible microscopic energy on the atomic and molecular scale. For example, a room temperature glass of water sitting on a table has no apparent energy, either potential or kinetic . But on the microscopic scale it is a seething mass of high speed molecules. If the water were tossed across the room, this microscopic energy would not necessarily be changed when we superimpose an ordered large scale motion on the water as a whole.

Heat - Heat may be defined as energy in transit from a high temperature object to a lower temperature object. An object does not possess "heat"; the appropriate term for the microscopic energy in an object is internal energy. The internal energy may be increased by transferring energy to the object from a higher temperature (hotter) object - this is called heating.

Work - When work is done by a thermodynamic system, it is usually a gas that is doing the work. The work done by a gas at constant pressure is W = p dV, where W id work, p is pressure and dV is change in volume. For non-constant pressure, the work can be visualized as the area under the pressure-volume curve which represents the process taking place.

Heat Engines -Refrigerators, Heat pumps, Carnot cycle, Otto cycle

The change in internal energy of a system is equal to the head added to the system minus the work done by the system:

dE = Q - W         (2)
where
dE = change in internal energy
Q = heat added to the system
W = work done by the system

1^st law does not provide the information of direction of processes and does not determine the final equilibrium state. Intuitively, we know that energy flows from high temperature to low temperature. Thus, the 2^nd law is needed to determine the direction of processes.
Enthalpy is the "thermodynamic potential" useful in the chemical thermodynamics of reactions and non-cyclic processes. Enthalpy is defined by

H = U + PV         (3)
where
H = enthalpy
U = internal energy
P = pressure
V = volume

Enthalpy is then a precisely measurable state variable, since it is defined in terms of three other precisely definable state variables.
There are two classical statements of the second law of thermodynamics:

Kelvin & Planc "No (heat) engine whose working fluid undergoes a cycle can absorb heat from a single reservoir, deliver an equivalent amount of work, and deliver no other effect"

Clausius "No machine whose working fluid undergoes a cycle can absorb heat from one system, reject heat to another system and produce no other effect"

Both statements of the second law place constraints on the first law by identifying that energy goes downhill.
The second law is concerned with entropy (S). Entropy is produced by all processes and associated with the entropy production is the loss of ability to do work. The second law says that the entropy of the universe increases. An increase in overall disorder is therefore spontaneous. If the volume and energy of a system are constant, then every change to the system increases the entropy. If volume or energy change, then the entropy of the system actually decrease. However, the entropy of the universe does not decrease.
For energy to be available there must be a region with high energy level and a region with low energy level. Useful work must be derived from the energy that would flows from the high level to the low level.

• 100% of the energy can not be transformed to work
• Entropy can be produced but never destroyed

Efficiency of a heat machine

The efficiency of a heat machine working between two energy levels is defined in terms of absolute temperature:

η = ( T_h - T_c ) / T_h = 1 - T_c / T_h(1)
where
η = efficiency
T_h = temperature high level (K)
T_c = temperature low level (K)

As a consequence, to attain maximum efficiency the T_c would have to be as cold as possible. For 100% efficiency the T_c would have to equal 0 K. This is practically impossible, so the efficiency is always less than 1 (less than 100%).

Change in entropy > 0 irreversible process

Change in entropy = 0 reversible process

Change in entropy < 0 impossible process

Entropy is used to define the unavailable energy in a system. Entropy defines the relative ability of one system to act on an other. As things move toward a lower energy level, where one is less able to act upon the surroundings, the entropy is said to increase.

• For the universe as a whole the entropy is increasing!

Entropy definition

Entropy is defined as :

S = H / T (2)
where
S = entrophy (kJ/kg K)
H = enthalpy (kJ/kg)
T = absolute temperature (K)

A change in the entropy of a system is caused by a change in its heat content, where the change of entropy is equal to the heat change divided by the average absolute temperature (T_a):

dS = dH / T_a (3)

The sum of (H / T) values for each step in the Carnot cycle equals 0. This only happens because for every positive H there is a countering negative H, overall.

Carnot Heat Cycle In a heat engine, a gas is reversibly heated and then cooled. A model of the cycle is as follows: State 1 --(isothermal expansion) --> State 2 --(adiabatic expansion) --> State 3 --(isothermal compression) --> State 4 --(adiabatic compression) --> State 1 State 1 to State 2: Isothermal Expansion Isothermal expansion occurs at a high temperature Th, dT = 0 and dE1 = 0. Since dE = H + w, w1 = - H1. For ideal gases, dE is dependent on temperature only. State 2 to State 3: Adiabatic Expansion The gas is cooled from the high temperature, Th, to the low temperature, Tc. dE2 = w2 and H2 = 0 (adiabatic). State 3 to State 4: Isothermal Compression This is the reverse of the process between states 1 and 2. The gas is compressed at Tc. dT = 0 and dE3 = 0. w3 = - H3 State 4 to State 1: Adiabatic Compression This is the reverse of the process between states 2 and 3. dE4 = w4 and H4 = 0 (adiabatic). The processes in the Carnot cycle can be graphed as the pressure vs. the volume. The area enclosed in the curve is then the work for the Carnot cycle because w = - integral (P dV). Since this is a cycle, dE overall equals 0. Therefore, -w = H = H1 + H2 + H3 + H4 If you decrease Tc, then the quantity -w gets larger in magnitude. if -w > 0 then H > 0 and the system, the heat engine, does work on the surroundings.

The laws of thermodynamics were determined empirically (by experiment). They are generalizations of repeated scientific experiments. The second law is a generalization of experiments dealing with entropy--it is that the dS of the system plus the dS of the surroundings is equal to or greater then 0.

• Entropy is not conserved like energy!

Example - Entropy Heating Water

A process raises 1 kg of water from 0 to 100^oC (273 to 373 K) under atmospheric conditions.

Specific enthalpy at 0^oC (h_f) = 0 kJ/kg (from steam tables) (Specific - per unit mass)

Specific enthalpy of water at 100^oC (h_f) = 419 kJ/kg (from steam tables)
Change in specific entropy:

dS = dH / T_a
    = ((419 kJ/kg) - (0 kJ/kg)) / ((273 K + 373 K)/2)
    = 1.297 kJ/kgK

Example - Entropy Evaporation Water to Steam

A process changes 1 kg of water at 100^oC (373 K) to saturated steam at 100^oC (373 K) under atmospheric conditions.

Specific enthalpy of steam at 100^oC (373 K) before evaporating = 0 kJ/kg (from steam tables)
Specific enthalpy of steam at 100^oC (373 K) after evaporating = 2 258 kJ/kg (from steam tables)

Change in specific entropy:

dS = dH / T_a
    = (2 258 - 0) / ((373 + 373)/2)
    = 6.054 kJ/kgK

The total change in specific entropy from water at 0^oC to saturated steam at 100^oC is the sum of the change in specific entropy for the water, plus the change of specific entropy for the steam.

Example - Entropy Superheated Steam

A process superheats 1 kg of saturated steam at atmospheric pressure to 150^oC (423 K).
Specific total enthalpy of steam at 100^oC (373 K) = 2 675 kJ/kg (from steam tables)

Specific total enthalpy of superheated steam at 150^oC (373 K) = 2 777 kJ/kg (from steam tables)

Change in specific entropy:

dS = dH / T_a
    = ((2777 kJ/kg) - (2675 kJ/kg)) / ((423 K + 373 K)/2)
    = 0.256 kJ/kgK