Guide Work Out Engineering Thermodynamics

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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 first law is the starting point for the science of thermodynamics and for engineering analysis. 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 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 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. When work is done by a thermodynamic system, it is usually a gas that is doing the work. For non-constant pressure, the work can be visualized as the area under the pressure-volume curve which represents the process taking place.

The change in internal energy of a system is equal to the head added to the system minus the work done by the system:. Intuitively, we know that energy flows from high temperature to low temperature. List is empty. Account Log in Registration. Work Out Engineering Thermodynamics by G. In Stock. Very Good Good Well Read. Qty: Add to cart.

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Free delivery in the US Read more here. Every used book bought is one saved from landfill. So far we have looked at the work done to compress fluid in a system.

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Suppose we have to introduce some amount of fluid into the system at a pressure p. Remember from the definition of the system that matter can enter or leave an open system. Consider a small amount of fluid of mass dm with volume dV entering the system. Suppose the area of cross section at the entrance is A. This value of pv is called the flow energy. The amount of work done in a process depends on the irreversibilities present. A complete discussion of the irreversibilities is only possible after the discussion of the second law.

The equations given above will give the values of work for quasi-static processes, and many real world processes can be approximated by this process. However, note that work is only done if there is an opposing force in the boundary, and that a volume change is not strictly required. If the system changes its states from 1 to 2, the work done is given by. Before thermodynamics was an established science, the popular theory was that heat was a fluid, called caloric , that was stored in a body.

Thus, it was thought that a hot body transferred heat to a cold body by transferring some of this fluid to it. However, this was soon disproved by showing that heat was generated when drilling bores of guns, where both the drill and the barrel were initially cold. Heat is the energy exchanged due to a temperature difference. As with work, heat is defined at the boundary of a system and is a path function.

Heat rejected by the system is negative, while the heat absorbed by the system is positive. The specific heat of a substance is the amount of heat required for a unit rise in the temperature in a unit mass of the material. If this quantity is to be of any use, the amount of heat transferred should be a linear function of temperature.

This is certainly true for ideal gases. This is also true for many metals and also for real gases under certain conditions. Since it was customary to give the specific heat as a property in describing a material, methods of analysis came to rely on it for routine calculations.

However, since it is only constant for some materials, older calculations became very convoluted for newer materials. Calculating specific heat requires us to specify what we do with Volume and Pressure when we change temperature. When Volume is fixed, it is called specific heat at constant volume C v. When Pressure is fixed, it is called specific heat at constant pressure C p. It can be seen that the specific heat as defined above will be infinitely large for a phase change, where heat is transferred without any change in temperature.

Thus, it is much more useful to define a quantity called latent heat , which is the amount of energy required to change the phase of a unit mass of a substance at the phase change temperature. A gas contained in an insulated vessel undergoes an adiabatic process. Adiabatic processes also take place even if the vessel is not insulated if the process is fast enough that there is not enough time for heat to escape e.

Adiabatic processes are also ideal approximations for many real processes, like expansion of a vapor in a turbine, where the heat loss is much smaller than the work done. It is well known that heat and work both change the energy of a system.

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Joule conducted a series of experiments which showed the relationship between heat and work in a thermodynamic cycle for a system. He used a paddle to stir an insulated vessel filled with fluid. Later, this vessel was placed in a bath and cooled. The energy involved in increasing the temperature of the bath was shown to be equal to that supplied by the lowered weight. Joule also performed experiments where electrical work was converted to heat using a coil and obtained the same result. The first law states that when heat and work interactions take place between a closed system and the environment, the algebraic sum of the heat and work interactions for a cycle is zero.

Q is the heat transferred, and W is the work done on or by the system. Since these are the only ways energy can be transferred, this implies that the total energy of the system in the cycle is a constant. One consequence of the statement is that the total energy of the system is a property of the system. This leads us to the concept of internal energy. In thermodynamics, the internal energy is the energy of a system due to its temperature. The statement of first law refers to thermodynamic cycles.

Using the concept of internal energy it is possible to state the first law for a non-cyclic process. Since the first law is another way of stating the conservation of energy, the energy of the system is the sum of the heat and work input, i. Here E represents the internal energy U of the system along with the kinetic energy KE and the potential energy PE and is called the total energy of the system. The KE and PE terms are relative to an external reference point i. Thermodynamics does not define the nature of the internal energy, but it can be rationalised using other theories i.

For gases, the value of KE and PE is quite small, so the important term is the internal energy function U. In particular, since for an ideal gas the state can be specified using two variables, the state variable u is given by u v, T , where v is the specific volume and T is the temperature.

Introducing this temperature dependence explicitly is important in many calculations. A constant-pressure heat capacity will be defined later, and it is important to keep them straight. The important point here is that the other variable that U depends on "naturally" is v, so to isolate the temperature dependence of U you want to take the derivative at constant v.

In the previous section, the internal energy of an ideal gas was shown to be a function of both the volume and temperature. Joule performed an experiment where a gas at high pressure inside a bath at the same temperature was allowed to expand into a larger volume.


In the above image, two vessels, labeled A and B, are immersed in an insulated tank containing water. A thermometer is used to measure the temperature of the water in the tank. The two vessels A and B are connected by a tube, the flow through which is controlled by a stop. Initially, A contains gas at high pressure, while B is nearly empty. The stop is removed so that the vessels are connected and the final temperature of the bath is noted. The temperature of the bath was unchanged at the end of the process, showing that the internal energy of an ideal gas was the function of temperature alone.

In particular, for a constant pressure process,. Since h , p , and t are state variables, c p is a state variable. Throttling is the process in which a fluid passing through a restriction loses pressure. It usually occurs when fluid passes through small orifices like porous plugs. The original throttling experiments were conducted by Joule and Thompson. As seen in the previous section, in adiabatic throttling the enthalpy is constant. What is significant is that for ideal gases, the enthalpy depends only on temperature, so that there is no temperature change, as there is no work done or heat supplied.

However, for real gases, below a certain temperature, called the inversion point , the temperature drops with a drop in pressure, so that throttling causes cooling, i. The first law is a statement of energy conservation. The rise in temperature of a substance when work is done is well known. Thus work can be completely converted to heat.


However, we observe that in nature, we don't see the conversion in the other direction spontaneously. The statement of the second law is facilitated by using the concept of heat engines. Heat engines work in a cycle and convert heat into work.

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A thermal reservoir is defined as a system which is in equilibrium and large enough so that heat transferred to and from it does not change its temperature appreciably. Heat engines work between two thermal reservoirs, the low temperature reservoir and the high temperature reservoir. The performance of a heat engine is measured by its thermal efficiency , which is defined as the ratio of work output to heat input, i.

Heat pumps transfer heat from a low temperature reservoir to a high temperature reservoir using external work, and can be considered as reversed heat engines. In other words, "It is impossible to have a heat engine which works in cycle and does work by exchanging heat with only one reservoir.

In other words, "It is impossible for heat to flow from a low temperature sink to a high temperature source without external work. A perpetual motion machine of the second kind , or PMM2 is one which converts all the heat input into work while working in a cycle.

Kelvin-Planck from Clausius. Suppose we can construct a heat pump which transfers heat from a low temperature reservoir to a high temperature one without using external work. Then, we can couple it with a heat engine in such a way that the heat removed by the heat pump from the low temperature reservoir is the same as the heat rejected by the heat engine, so that the combined system is now a heat engine which converts heat to work without any external effect.

This is thus in violation of the Kelvin-Planck statement of the second law. Clausius from Kelvin-Planck. Now suppose we have a heat engine which can convert heat into work without rejecting heat anywhere else. We can combine it with a heat pump so that the work produced by the engine is used by the pump. Now the combined system is a heat pump which uses no external work, violating the Clausius statement of the second law. Thus, we see that the Clausius and Kelvin-Planck statements are equivalent, and one necessarily implies the other.

Nicholas Sadi Carnot devised a reversible cycle in called the Carnot cycle for an engine working between two reservoirs at different temperatures. It consists of two reversible isothermal and two reversible adiabatic processes. For a cycle , the working material. Heat is transferred to the working material during Q 1 and heat is rejected during Q 2.

The proof by contradiction of the above statements come from the second law, by considering cases where they are violated. For instance, if you had a Carnot engine which was more efficient than another one, we could use that as a heat pump since processes in a Carnot cycle are reversible and combine with the other engine to produce work without heat rejection, to violate the second law. Lord Kelvin used Carnot's principle to establish the thermodynamic temperature scale which is independent of the working material. As shown in the previous section, the ratio of heat transferred only depends on the temperatures.

Considering reservoirs 1 and The thermodynamic temperature scale is also known as the Kelvin scale, and it needs only one fixed point, as the other one is absolute zero. The concept of absolute zero will be further refined during the statement of the third law of thermodynamics. Reservoirs are systems of large quantity of matter which no temperature difference will occur when finite amount of heat is transferred or removed.

Examples of reservoirs are atmosphere, oceans, seas etc. Clausius theorem states that any reversible process can be replaced by a combination of reversible isothermal and adiabatic processes. Consider a reversible process a-b. A series of isothermal and adiabatic processes can replace this process if the heat and work interaction in those processes is the same as that in the process a-b.

Let this process be replaced by the process a-c-d-b , where a-c and d-b are reversible adiabatic processes, while c-d is a reversible isothermal process. The isothermal line is chosen such that the area a-e-c is the same as the area b-e-d. Now, since the area under the p-V diagram is the work done for a reversible process, we have, the total work done in the cycle a-c-d-b-a is zero.

Applying the first law, we have, the total heat transferred is also zero as the process is a cycle. Since a-c and d-b are adiabatic processes, the heat transferred in process c-d is the same as that in the process a-b. Now applying first law between the states a and b along a-b and a-c-d-b , we have, the work done is the same. Thus the heat and work in the process a-b and a-c-d-b are the same and any reversible process a-b can be replaced with a combination of isothermal and adiabatic processes, which is the Clausius theorem.

A corollary of this theorem is that any reversible cycle can be replaced by a series of Carnot cycles. Suppose each of these Carnot cycles absorbs heat dQ 1 i at temperature T 1 i and rejects heat dQ 2 i at T 2 i. The negative sign is included as the heat lost from the body has a negative value. Summing over a large number of these cycles, we have, in the limit,. Further, using Carnot's principle, for an irreversible cycle, the efficiency is less than that for the Carnot cycle, so that. As the heat is transferred out of the system in the second process, we have, assuming the normal conventions for heat transfer,.

The above inequality is called the inequality of Clausius. Here the equality holds in the reversible case. Entropy is the quantitative statement of the second law of thermodynamics. It is represented by the symbol S , and is defined by. Note that as we have used the Carnot cycle, the temperature is the reservoir temperature. However, for a reversible process, the system temperature is the same as the reversible temperature. Consider a system undergoing a cycle , where it returns to the original state along a different path.

Since entropy of the system is a property, the change in entropy of the system in and are numerically equal. Suppose reversible heat transfer takes place in process and irreversible heat transfer takes place in process Applying Clausius's inequality, it is easy to see that the heat transfer in process dQ irr is less than T dS. That is, in an irreversible process the same change in entropy takes place with a lower heat transfer. As a corollary, the change in entropy in any process, dS , is related to the heat transfer dQ as. This is called the principle of increase of entropy and is an alternative statement of the second law.

Since T and S are properties, you can use a T-S graph instead of a p-V graph to describe the change in the system undergoing a reversible cycle. Thus the area under the T-S graph is the work done by the system. Further, the reversible adiabatic processes appear as vertical lines in the graph, while the reversible isothermal processes appear as horizontal lines.

As a general rule, all things being equal, entropy increases as, temperature increases and as pressure and concentration decreases and energy stored as internal energy has higher entropy than energy which is stored as kinetic energy. From the second law of thermodynamics, we see that we cannot convert all the heat energy to work.

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If we consider the aim of extracting useful work from heat, then only some of the heat energy is available to us. It was previously said that an engine working with a reversible cycle was more efficient than an irreversible engine. Now, we consider a system which interacts with a reservoir and generates work, i.

Consider a system interacting with a reservoir and doing work in the process. Suppose the system changes state from 1 to 2 while it does work. We have, according to the first law,. Since it is a property, it is the same for both the reversible and irreversible process. For an irreversible process, it was shown in a previous section that the heat transferred is less than the product of temperature and entropy change. Thus the work done in an irreversible process is lower, from first law.

The availability function gives the effectiveness of a process in producing useful work. The above definition is useful for a non-flow process. For a flow process, it is given by. Maximum work can be obtained from a system by a reversible process. The work done in an actual process will be smaller due to the irreversibilities present.

The difference is called the irreversibility and is defined as. The Helmholtz free energy is relevant for a non-flow process. For a flow process, we define the Gibbs Free Energy. The Helmholtz and Gibbs free energies have applications in finding the conditions for equilibrium. Entropy is zero only in a perfect crystal at absolute zero 0 kelvin [- At a temperature of absolute zero there is no thermal energy or heat.

At a temperature of zero Kelvin the atoms in a pure crystalline substance are aligned perfectly and do not move. There is no entropy of mixing since the substance is pure. By -VBM. All materials can exist in three phases: solid , liquid , and gas. All one component systems share certain characteristics, so that a study of a typical one component system will be quite useful. For this analysis, we consider heat transferred to the substance at constant pressure. The above chart shows temperature vs. The three line-curves labeled p 1 , p 2 , and p c above are isobars, showing conditions at constant pressure.

When the liquid and vapor coexist, it is called a saturated state.