Thermodynamic system: 2010

Thermodynamic system

In thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration. Anything under consideration is called a system. A hypothetical boundary separates the system from the rest of the universe, which is referred to as the environment, surroundings, or reservoir. A useful classification of thermodynamic systems is based on the nature of the boundary and the quantities flowing through it, such as matter, energy, work, heat, and entropy. A system can be anything, for example a piston, a solution in a test tube, a living organism, an electrical circuit, a planet, etc System boundary.svg

Overview

Thermodynamics is conducted under a system-centered view of the universe. All quantities, such as pressure or mechanical work, in an equation refer to the system unless labeled otherwise. Thermodynamics is basically concerned with the flow and balance of energy and matter in a thermodynamic system. Three types of thermodynamic systems are distinguished depending on the kinds of interaction and energy exchange taking place between the system and its surrounding environment:

Isolated systems are completely isolated in every way from their environment. They do not exchange heat, work or matter with their environment. An example of an isolated system would be an insulated rigid container, such as an insulated gas cylinder.

Closed systems are able to exchange energy (heat and work) but not matter with their environment. A greenhouse is an example of a closed system exchanging heat but not work with its environment. Whether a system exchanges heat, work or both is usually thought of as a property of its boundary.

Open systems: exchanging energy (heat and work) and matter with their environment. A boundary allowing matter exchange is called permeable. The ocean would be an example of an open system.

In reality, a system can never be absolutely isolated from its environment, because there is always at least some slight coupling, even if only via minimal gravitational attraction. In analyzing a system in steady-state, the energy into the system is equal to the energy leaving the system [1].

As an example, consider the system of hot liquid water and solid table salt in a sealed, insulated test tube held in a vacuum (the surroundings). The test tube constantly loses heat (in the form of black-body radiation), but the heat loss progresses very slowly. If there is another process going on in the test tube, for example the dissolution of the salt crystals, it will probably occur so quickly that any heat lost to the test tube during that time can be neglected. (Thermodynamics does not measure time, but it does sometimes accept limitations on the timeframe of a process.)

History of term

The first to develop the concept of a "thermodynamic system" was the French physicist Sadi Carnot whose 1824 Reflections on the Motive Power of Fire studied what he called the "working substance" (system), i.e. typically a body of water vapor, in steam engines, in regards to the system's ability to do work when heat is applied to it. The working substance could be put in contact with either a heat reservoir (a boiler), a cold reservoir (a stream of cold water), or a piston (to which the working body could do work by pushing on it). In 1850, the German physicist Rudolf Clausius generalized this picture to include the concept of the surroundings, and began referring to the system as a "working body." In his 1850 manuscript On the Motive Power of Fire, Clausius wrote:

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"With every change of volume (to the working body) a certain amount work must be done by the gas or upon it, since by its expansion it overcomes an external pressure, and since its compression can be brought about only by an exertion of external pressure. To this excess of work done by the gas or upon it there must correspond, by our principle, a proportional excess of heat consumed or produced, and the gas cannot give up to the "surrounding medium" the same amount of heat as it receives."

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The article Carnot heat engine shows the original piston-and-cylinder diagram used by Carnot in discussing his ideal engine; below, we see the Carnot engine as is typically modeled in current use:

Carnot engine diagram (modern) - where heat flows from a high temperature T_H furnace through the fluid of the "working body" (working substance) and into the cold sink T_C, thus forcing the working substance to do mechanical work W on the surroundings, via cycles of contractions and expansions.

In the diagram shown, the "working body" (system), a term introduced by Clausius in 1850, can be any fluid or vapor body through which heat Q can be introduced or transmitted through to produce work. In 1824, Sadi Carnot, in his famous paper Reflections on the Motive Power of Fire, had postulated that the fluid body could be any substance capable of expansion, such as vapor of water, vapor of alcohol, vapor of mercury, a permanent gas, or air, etc. Although, in these early years, engines came in a number of configurations, typically Q_H was supplied by a boiler, wherein water was boiled over a furnace; Q_C was typically a stream of cold flowing water in the form of a condenser located on a separate part of the engine. The output work W here is the movement of the piston as it is used to turn a crank-arm, which was then typically used to turn a pulley so to lift water out of flooded salt mines. Carnot defined work as "weight lifted through a height."

Systems in equilibrium

In isolated systems it is consistently observed that as time goes on internal rearrangements diminish and stable conditions are approached. Pressures and temperatures tend to equalize, and matter arranges itself into one or a few relatively homogeneous phases. A system in which all processes of change have gone practically to completion is considered to be in a state of thermodynamic equilibrium. The thermodynamic properties of a system in equilibrium are unchanging in time. Equilibrium system states are much easier to describe in a deterministic manner than non-equilibrium states.

In thermodynamic processes, large departures from equilibrium during intermediate steps are associated with increases in entropy and increases in the production of heat rather than useful work. It can be shown that for a process to be reversible, each step in the process must be reversible. For a step in a process to be reversible, the system must be in equilibrium throughout the step. That ideal cannot be accomplished in practice because no step can be taken without perturbing the system from equilibrium, but the ideal can be approached by making changes slowly.

Open systems

In open systems, matter may flow in and out of the system boundaries. The first law of thermodynamics for open systems states: the increase in the internal energy of a system is equal to the amount of energy added to the system by matter flowing in and by heating, minus the amount lost by matter flowing out and in the form of work done by the system. The first law for open systems is given by:

During steady, continuous operation, an energy balance applied to an open system equates shaft work performed by the system to heat added plus net enthalpy added.

$\mathrm{d}U=\mathrm{d}U_{in}+\delta Q-\mathrm{d}U_{out}-\delta W\,$

where U_in is the average internal energy entering the system and U_out is the average internal energy leaving the system

The region of space enclosed by open system boundaries is usually called a control volume, and it may or may not correspond to physical walls. If we choose the shape of the control volume such that all flow in or out occurs perpendicular to its surface, then the flow of matter into the system performs work as if it were a piston of fluid pushing mass into the system, and the system performs work on the flow of matter out as if it were driving a piston of fluid. There are then two types of work performed: flow work described above which is performed on the fluid (this is also often called PV work) and shaft work which may be performed on some mechanical device. These two types of work are expressed in the equation:

$\delta W=\mathrm{d}(P_{out}V_{out})-\mathrm{d}(P_{in}V_{in})+\delta W_{shaft}\,$

Substitution into the equation above for the control volume cv yields:

$\mathrm{d}U_{cv}=\mathrm{d}U_{in}+\mathrm{d}(P_{in}V_{in}) - \mathrm{d}U_{out}-\mathrm{d}(P_{out}V_{out})+\delta Q-\delta W_{shaft}\,$

The definition of enthalpy, H, permits us to use this thermodynamic potential to account for both internal energy and PV work in fluids for open systems:

$\mathrm{d}U_{cv}=\mathrm{d}H_{in}-\mathrm{d}H_{out}+\delta Q-\delta W_{shaft}\,$

During steady-state operation of a device (see turbine, pump, and engine), any system property within the control volume is independent of time. Therefore, the internal energy of the system enclosed by the control volume remains constant, which implies that dU_cv in the expression above may be set equal to zero. This yields a useful expression for the power generation or requirement for these devices in the absence of chemical reactions:

$\frac{\delta W_{shaft}}{\mathrm{d}t}=\frac{\mathrm{d}H_{in}}{\mathrm{d}t}- \frac{\mathrm{d}H_{out}}{\mathrm{d}t}+\frac{\delta Q}{\mathrm{d}t} \,$

This expression is described by the diagram above.

Closed Systems

In a closed system, no mass may be transferred in or out of the system boundaries. The system will always contain the same amount of matter, but heat and work can be exchanged across the boundary of the system. Whether a system can exchange heat, work, or both is dependent on the property of it boundary.

Adiabatic boundary – not allowing any heat exchange
Rigid boundary – not allowing exchange of work

One example is fluid being compressed by a piston in a cylinder. Another example of a closed system is a bomb calorimeter, a type of constant-volume calorimeter used in measuring the heat of combustion of a particular reaction. Electrical energy travels across the boundary to produce a spark between the electrodes and initiates combustion. Heat transfer occurs across the boundary after combustion but no mass transfer takes place either way.

Beginning with the first law of thermodynamics for an open system, this is expressed as:

$\mathrm{d}U=Q-W+m_{i}(h+\frac{1}{2}v^2+gz)_{i}-m_{e}(h+\frac{1}{2}v^2+gz)_{e}$

where U is internal energy, Q is heat transfer, W is work, and since no mass is transferred in or out of the system, both expressions involving mass flow, , zeroes, and the first law of thermodynamics for a closed system is derived. The first law of thermodynamics for a closed system states that the amount of internal energy within the system equals the difference between the amount of heat added to or extracted from the system and the wok done by or to the system. The first law for closed systems is stated by:

d U = δ Q - δ W

where U is the average internal energy within the system, Q is the heat added to or extracted from the system and W is the work done by or to the system.

Substituting the amount of work needed to accomplish a reversible process, which is stated by:

δ W = P d V

where P is the measured pressure and V is the volume, and the heat required to accomplish a reversible process stated by the second law of thermodynamics, the universal principle of entropy, stated by:

δ Q = T d S

where T is the absolute temperature and S is the entropy of the system, derives the fundamental thermodynamic relationship used to compute changes in internal energy, which is expressed as:

δ U = T d S + P d V

The second law of thermodynamics is only true for closed systems. It states that the entropy of an isolated system not in equilibrium will tend to increase over time, approaching maximum value at equilibrium. Overall, in a closed system, the available energy can never increase, and it complement, entropy, can never decrease.

An isolated system is a type of closed system that does not interact with its surroundings in any way. Mass and energy remains constant within the system, and no energy or mass transfer takes place across the boundary.

Thermodynamic system

Monday, April 19, 2010