The First and Second Laws

Much of thermodynamics concerns the causes and consequences of changing the state of a system. For example, you may be confronted with a polymerization process that converts esters to polyesters for the textile industry, or you may need a process that removes heat from a chemical reactor to control the reaction temperature and thereby control the rate of reaction. You may need a process that pressurizes a petroleum feed to a flash distillation unit, or you may need a process that recycles plastic bottles into garbage bags. In these and a multitude of other such situations, a system is to be subjected to a process that converts an initial state into some final state. 

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Derive Eq. III-21 from the first and second laws of thermodynamics and related definitions. 

Equation (A2.1.21) includes, as a special case, the statement dS > 0 for adiabatic processes (for which Dq = 0) and, a fortiori, the same statement about processes that may occur in an isolated system (Dq = T)w = 0). If the universe is an isolated system (an assumption that, however plausible, is not yet subject to experimental verification), the first and second laws lead to the famous statement of Clausius The energy of the universe is constant the entropy of the universe tends always toward a maximum. ... 

In the Lewis and Gibson statement of the third law, the notion of a perfect crystalline substance , while understandable, strays far from the macroscopic logic of classical thennodynamics and some scientists have been reluctant to place this statement in the same category as the first and second laws of thennodynamics. Fowler and Guggenheim (1939), noting drat the first and second laws both state universal limitations on processes that are experunentally possible, have pointed out that the principle of the unattainability of absolute zero, first enunciated by Nemst (1912) expresses a similar universal limitation ... 

Accurate temperature measurements in real-life situations are difficult to make using the KTTS. Most easily used thermometers are not thermodynamic that is, they do not operate on principles of the first and second laws. Most practicable thermometers depend upon some principle that is a repeatable and single-valued analogue of temperature, and they are used as interpolation devices of practical and utilitarian temperature scales which are themselves... 

The foUowiag criterion of phase equUibrium can be developed from the first and second laws of thermodynamics the equUibrium state for a closed multiphase system of constant, uniform temperature and pressure is the state for which the total Gibbs energy is a minimum, whence... 

In the broadest sense, thermodynamics is concerned with mathematical relationships that describe equiUbrium conditions as well as transformations of energy from one form to another. Many chemical properties and parameters of engineering significance have origins in the mathematical expressions of the first and second laws and accompanying definitions. Particularly important are those fundamental equations which connect thermodynamic state functions to real-world, measurable properties such as pressure, volume, temperature, and heat capacity (1 3) (see also Thermodynamic properties). 

Fundamental Property Relation. The fundamental property relation, which embodies the first and second laws of thermodynamics, can be expressed as a semiempifical equation containing physical parameters and one or more constants of integration. AH of these may be adjusted to fit experimental data. The Clausius-Clapeyron equation is an example of this type of relation (1—3). 

Funda.menta.1 PropertyRela.tion. For homogeneous, single-phase systems the fundamental property relation (3), is a combination of the first and second laws of thermodynamics that may be written as... 

The fundamental thermodynamic properties that arise in connection with the first and second laws of thermodyuamics are internal energy and entropy These properties, together with the two laws for which they are essential, apply to all types of systems. However, different types of systems are characterized by different sets of measurable coordinates or variables. The type of system most commonly... 

Consider a closed PVT system, either homogeneous or heterogeneous, of uniform T and P, which is in thermal and mechanical equilibrium with its surroundings, but which is not initially at internal equilibrium with respect to mass transfer or with respect to chemical reaction. Changes occurring in the system are then irreversible, and must necessarily bring the system closer to an equihbrium state. The first and second laws written for the entire system are... 

In his first work on thermodynamics in 1873, Gibbs immediately combined the differential forms of the first and second laws of thermodynamics for the reversible processes of a system to obtain a single Tundamciital equation ... 

An estimate of the efficiency of a heat engine working between two temperatures T and T - can be obtained by assuming the Carnot cycle is used. By combining the results from applying the first and second laws to the Carnot cycle, the Carnot efficiency e, may be written ... 

In fluid mechanics the principles of conservation of mass, conservation of momentum, the first and second laws of thermodynamics, and empirically developed correlations are used to predict the behavior of gases and liquids at rest or in motion. The field is generally divided into fluid statics and fluid dynamics and further subdivided on the basis of compressibility. Liquids can usually be considered as incompressible, while gases are usually assumed to be compressible. 

The heat capacity of a substance is extremely important in thermodynamic analysis involving both the first and second laws. 

A heat pump, which is the opposite of a heat engine, uses work energy to transfer heat from a cold reservoir to a hot reservoir. In households, the cold reservoir is often the surrounding air or the ground while the hot reservoir is the home. For an ideal heat pump system with Qj and T[ referring to the hot reservoir and Q2 and Tj referring to the cold reservoir, the work required is, from the first and second laws. 

Refrigerating machines absorb heat from a cold reservoir at temperature T and discharge heat Q, into a hot reservoir at T. To accomplish this, work energy must also be absorbed. The minimum required work is obtained as shown before, using the first and second laws ... 

The first and second law expressions can be combined and written for constant temperature, constant pressure processes ... 

The physical laws of thermodynamics, which define their efficiency and system dynamics, govern compressed-air systems and compressors. This section discusses both the first and second laws of thermodynamics, which apply to all compressors and compressed-air systems. Also applying to these systems are the ideal gas law and the concepts of pressure and compression. 

In addition, application of the first and second laws (equations 20.128 and 20.138) gives... 

Our most important insight into the connection between thermodynamics and black holes comes from a celebrated result obtained by Bardeen, Carter and Hawking [bard73], that the four laws of black hole physics can be obtained by replacing, in the first and second laws of thermodynamics, the entropy and temperature of a thermodynamical system by the black hole event horizon (or boundary of the black hole) and surface gravity (which measures the strength of the gravitational field at the black hole s surface). 

In Chapter 1 we described the fundamental thermodynamic properties internal energy U and entropy S. They are the subjects of the First and Second Laws of Thermodynamics. These laws not only provide the mathematical relationships we need to calculate changes in U, S, H,A, and G, but also allow us to predict spontaneity and the point of equilibrium in a chemical process. The mathematical relationships provided by the laws are numerous, and we want to move ahead now to develop these equations.1... 

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