## Thermodynamics

### Contents

Terminology
The Four Laws of Thermodynamics
Entropy
Systems
States
Thermodynamic Process
Work and Engines
Connection to the Microscopic View
Non-equilibrium Thermodynamics & Life (2020)

### Terminology

Thermodynamics is the branch of science that deals with the conversions of various forms of energy and the effect on the state of a system. It was developed in the 19th century, when it was of great practical importance in the era of steam engines. Since the microscopic structure of matter is not known at that time, it can only prescribe a macroscopic view. It remains valid and useful in the 21th century, but now we understand such macroscopic description is just the averaged behaviour of a large collection of microscopic constituents.

It is essential to define the terminology before learning more about the subject:

• Heat - Heat (Q) is a form of energy transfer associated with random motion of the microscopic particles.
• Work - Work (W) is the organized form of energy transfer associated with the motion of microscopic particles as a whole (in a certain direction), e.g., the expanding gas that propels a piston.
• Internal Energy - The internal energy (U) of a system is the total energy due to the motion of molecules, plus the rotation, and vibration of atoms within molecules. Heat and work are two methods of adding energy to or subtracting energy from a system. They represent energy in transit and are the terms used when energy is moving. Once the transfer of energy is over, the system is said to have undergone a change in internal energy dU. Thus, in terms of the amount of heat dQ and work dW:

dU = dQ - dW ---------- (1)

where dQ and -dW are positive for energy transfer from the surroundings to the system, and negative for energy transfer from the system to the surroundings. If the process of energy transfer is broken down into finer details, e.g., change in disorder (dS), volume expansion/contraction (dV), and adding more particles (dN), then the change in internal energy can be expressed as:

dU = T dS - p dV + dN ---------- (2)

where is the chemical potential.

• Free Energy - The amount of available energy that is capable of performing work.
• Temperature - Temperature (T) is related to the amount of internal energy in a system. As more heat or work is added the temperature rises, similarly a decrease in temperature corresponds to a loss of heat or work performed from the system. Temperature is an intrinsic property of a system, meaning that it does not depend on the system size or the amount of material in the system. Other intrinsic properties include pressure and density. The internal energy (U) is related to the temperature (T) by the formula:

U = nRT ---------- (3)

where R = 8.314x107 erg/Ko-mole is called the gas constant.

• Pressure - Pressure (p) is the force normal to the surface of area upon which it exerts. Microscopically, it is the transfer of momenta from the particles that produces the force on the surface.
• Volume - Volume (V) is referred to the three dimensional space occupied by the system.
• Particle Number - Particle number (N) is the number of a particular constituents in a system.
• Avogadro's Number - Avogadro's number (N0) is 6.023 x 1023. One mole is defined as the unit that contains that many number of particles such as atoms, molecules, or ions, e.g., it is the number of carbon-12 atoms in 12 gram of the substance, or the number of protons in 1 gram of the same substance, etc.
• Number of Moles - Number of moles (n) is the number of particles in the unit of a mole, i.e., n = N / N0.
• Density - Density ( ) is defined as mass per unit volume.
• Entropy - Entropy (S) is a measure of disorder in the system. Mathematically, the change of entropy dS is related to the amount of heat transfer dQ by the formula:

dS = dQ / T    or    dQ = T dS ---------- (4)

• Chemical Potential - The chemical potential ( ) of a thermodynamic system is the change in the energy of the system when a different kind of constituent particle is introduced, with the entropy and volume held fixed.
Some thermodynamics definitions here such as temperature, pressure, and density are specified under an equilibrium condition. The changes in these variables are idealized with a succession of equilibrium states. Many important biochemical and physical processes (such as in microfluid, chemical reactions, molecular folding, cell membranes, and cosmic expansion) operate far from equilibrium, where the standard theory of thermodynamics does not apply. Figure 01a shows the cases for different kinds of thermodynamic theory. Case 1 is for over all equilibrium in the system, which is described by classical thermodynamics. Case 2 has local equilibrium in different regions. A theory of nonequilibrium thermodynamics (using the concept of flow or flux) has been developed for such situation. In case 3 the molecules become a chaotic jumble such that the concept of temperature is not applicable anymore. A new theory has been formulated by using a

#### Figure 01a Thermodynamics Theory [view large image]

new set of variables within the very short timescale for the transformation. The second law of thermodynamics has been shown to be valid for all these cases.

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