Expansion of a gas

Figure A2.1.2. Reversible expansion of a gas witli the removal one-by-one of grains of sand atop a piston.

For example, the expansion of a gas requires the release of a pm holding a piston in place or the opening of a stopcock, while a chemical reaction can be initiated by mixing the reactants or by adding a catalyst. One often finds statements that at equilibrium in an isolated system (constant U, V, n), the entropy is maximized . Wliat does this mean ... 

As reservoir pressure is reduced by oil production, additional recovery mechanisms may operate. One such mechanism is natural water drive. Water from an adjacent more highly pressured formation is forced into the oil-bearing formation by the pressure differential between the formations. Another mechanism is gas drive. Expansion of a gas cap above the oil as oil pressure declines can also drive additional oil to the wellbore. Produced gas may be reinjected to maintain gas cap pressure as is done on the Alaskan North Slope. Additional oil may also be produced by compaction of the reservoir rock as oil production reduces reservoir pressure. 

Example The expansion of a gas behind a piston is characterized by the simultaneous equations... 

Instruments based on the contact principle can further be divided into two classes mechanical thermometers and electrical thermometers. Mechanical thermometers are based on the thermal expansion of a gas, a liquid, or a solid material. They are simple, robust, and do not normally require power to operate. Electrical resistance thermometers utilize the connection between the electrical resistance and the sensor temperature. Thermocouples are based on the phenomenon, where a temperature-dependent voltage is created in a circuit of two different metals. Semiconductor thermometers have a diode or transistor probe, or a more advanced integrated circuit, where the voltage of the semiconductor junctions is temperature dependent. All electrical meters are easy to incorporate with modern data acquisition systems. A summary of contact thermometer properties is shown in Table 12.3. 

In filled thermometers the thermal expansion of a gas or a liquid is transmitted through a thin capillary tube to a bellows or helix, where the deformation indicates the temperature. The temperature range of filled thermometers is very wide, approximately -200 to +700 °C. They are extremely robust but are not very high in accuracy. The application is mainly for process instrumentation and as stand-alone control devices. 

Isothermal change A process that takes place at constant temperature, such as the isothermal expansion of a gas. 

As an example of conditional irreversibility may be taken the expansion of a gas. Work is done by the change of bulk in opposition to the external forces, and heat is absorbed from the environment. The conditions which must hold in order that the process actually occurs are ... 

Now consider any reversible change which is not a cyclic change, as, for example, the expansion of a gas, or the evaporation of a liquid. 

Expansion of a Gas into a Vacuum.—If a gas is allowed to rush into a vacuous space, or into a space containing a gas under a less pressure, we have an example of a process attended by conditional irreversibility. 

Measurement of the expansion of a gas-liquid fluidized bed provides a measure of the holdup of solids or of the corresponding combined holdup of gas and liquid. From such measurements, the holdup of liquid may be calculated if the gas holdup has been determined independently. 

In this discussion, we will limit our writing of the Pfaffian differential expression bq, for the differential element of heat flow in thermodynamic systems, to reversible processes. It is not possible, generally, to write an expression for bq for an irreversible process in terms of state variables. The irreversible process may involve passage through conditions that are not true states" of the system. For example, in an irreversible expansion of a gas, the values of p. V, and T may not correspond to those dictated by the equation of state of the gas. 

The adiabatic expansion of a gas is an example of (b). In the reversible adiabatic expansion of one mole of an ideal monatomic gas, initially at 298.15 K, from a volume of 25 dm3 to a final volume of 50 dm3, 2343 J of energy are added into the surroundings from the work done in the expansion. Since no heat can be exchanged (in an adiabatic process, q = 0), the internal energy of the gas must decrease by 2343 J. As a result, the temperature of the gas falls to 188 K. 

A characteristic of the non-ideal gas is that it has a finite Joule-Thomson effect. This relates to the amount of heat which must be added during an expansion of a gas from a pressure Pi to a pressure P2 in order to maintain isothermal conditions. Imagine a gas flowing from a cylinder, fitted with a piston at a pressure Pi to a second cylinder at a pressure Pi (Figure 2.2). 

To calculate the work of reversible, isothermal expansion of a gas, we have to use calculus, starting at Eq. 3 written for an infinitesimal change in volume, dV ... 

In science, we look for patterns to discover nature s laws. What is the pattern common to all spontaneous changes To find a pattern, it is often best to start with very simple examples, because then the pattern is likely to be more obvious. So, let s think about two simple spontaneous changes—the cooling of a hot metal and the expansion of a gas—at a molecular level and search for their common feature. 

Thus, the cooling of hot metal is accompanied by an increase in entropy as energy spreads into the surroundings. The isolated system in this case is taken to be the block and its immediate surroundings. Likewise, the expansion of a gas is accompanied by an increase in entropy as the molecules spread through the container. 

These special cases include any isothermal process, such as isothermal expansion of a gas, and transfers of energy at freezing or boiling points (see Section 7.4). 

Thermometry is the science of measuring the temperature of a system or the ability of a system to transfer heat to emother system. Temperature mecisurement is important to a wide range of activities, including manufacturing, scientific research, and medical practice. Thermometry relates to the dilatrometric measurement in that the expansion of a gas, liquid or solid is used to determine temperature. 

An additional complication may arise in a few cases from the Joule-Thompson effect during expansion of a gas through a membrane changing the temperature. High-pressure CO2 is an example. 

The energy recoverable from the expansion of a gas can be estimated by assuming polytropic expansion see Section 3.13.2 and Example 3.17. 

A gas-gathering and transmission system consists of sources of gas, arcs composed of pipeline segments, compressor stations, and delivery sites. The design or expansion of a gas pipeline transmission system involves capital expenditures as well as the continuing cost of operation and maintenance. Many factors have to be considered, including... 

Derive an explicit expression for the work performed in the irreversible expansion of a gas from volume Vi to volume V2 against a constant external pressure P that is less than the pressure of the gas throughout the expansion. 

For a scientist, the primary interest in thermodynamics is in predicting the spontaneous direction of natural processes, chemical or physical, in which by spontaneous we mean those changes that occur irreversibly in the absence of restraining forces—for example, the free expansion of a gas or the vaporization of a hquid above its boiling point. The first law of thermodynamics, which is useful in keeping account of heat and energy balances, makes no distinction between reversible and irreversible processes and makes no statement about the natural direction of a chemical or physical transformation. 

The reversible expansion of a gas (a reversible flow of work) requires that the pressure of the gas differ only infinitesimally from the pressure of the surroundings. Similarly, a reversible flow of heat requires that the temperature of the system differ only infinitesimally from the temperature of the surroundings. If the temperature of the system is to change by a finite amount, then the temperature of the surroundings must change infinitely slowly. Thus, the reversible flow of heat, like the reversible expansion of a gas, is a limiting case that can be approached as closely as desired, but it can never be reached. 

If some work is done, e.g. expansion of a gas, q is less than AH. 

Figure 3.3 Compression and expansion of a gas to produce a sound wave...

We conclude by summarizing in Table 3.1 some key distinctions between reversible and irreversible processes, taking as an example the expansion of a gas against a piston, with external pressure Fext ... 

Figure 3.10 Schematic of Joule s experiment for irreversible expansion of a gas into an evacuated chamber in a water bath.

Golay cell Infrared detector that uses expansion of a gas in a blackened chamber to deform a flexible mirror. Deflection of a beam of light by the mirror changes the power impinging on a phototube. 

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