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| Kinds of Thermodynamic Processes |
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| In this section, we describe four specific kinds of thermodynamic processes that often occur in practical situations. These can be summarized briefly as “no heat transfer” or adiabatic, “constant volume” or isochoric, “constant pressure” or isobaric, and “constant temperature” or isothermal. For some of these, we can use a simplified form of the first law of thermodynamics. |
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| An adiabatic process is defined as one with no heat transfer into or out of a system: dQ=0. We can prevent heat flow either by surrounding the system with thermally insulating material or by carrying out the process so quickly that there is not enough time for appreciable heat flow. From the first law, we find that for every adiabatic process, |
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| dQ = dv + dw = 0, du = -dw |
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| when a system expands adiabatically. dW is positive (the system does work on its surroundings), so DU is negative and the internal energy decreases. When a system is compressed adiabatically, dW is negative (work is done on the system by its surroundings) and DU increases. In many (but not all) systems, an increase of internal energy is accompanied by a rise in temperature. |
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| The compression stroke in an internal-combustion engine is almost an adiabatic process. The temperature rises as the air-fuel mixture in the cylinder is compressed. The expansion of the burned fuel during the power stroke is also nearly an adiabatic expansion with a drop in temperature. |
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| An isochoric process is a constant-volume process. When the volume of a thermodynamic system is constant, it does zero work on the surroundings. Then W = 0, and |
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| In an isochoric process, all the energy added as heat remains in the system as an increase in internal energy. Heating a gas in a closed constant-volume container is an example of an isochoric process. (Note that there are types of work that do not involve a volume change. For example, we can do work on a fluid by stirring it. In some cases, “isochoric” is used to mean that no work is done). |
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| An isobaric process is a constant-pressure process. In general, none
of the three quantities DU, Q and dW is zero in
an isobaric process, but calculating W is easy nonetheless. |
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| W=p (V2-V1) (isobaric process) |
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| An isothermal process is a constant-temperature process. For a process to be isothermal, any heat flow into or out of the system must occur slowly enough so that thermal equilibrium is maintained. In general, none of the quantities DU, Q or dW is zero in an isothermal process. |
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| In some special cases, the internal energy of a system depends only on its temperature and not on its pressure or volume. The most familiar system having this special property is an ideal gas, which we will discuss in the next section. For such systems, if the temperature is constant, the internal energy is also constant; DU=0 and Q=W. That is, any energy entering the system as heat Q must leave it again as work W done by the system |
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| A hypothetical setup for studying the behavior of gases. |
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| The pressure p, volume V, temperature T
and number of moles of a gas can be controlled and measured using this
setup. |
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| The above figure shows a PV diagram for each of these four processes for a constant amount of an ideal gas. The path followed in an adiabatic process (a to l) is called an adiabat. A vertical line (constant volume) is an isochor, a horizontal line (constant pressure) is an isobar, and a curve of constant temperature (shown as light blue lines in the figure) is an isotherm. |
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| Consider a sample of an ideal gas kept in an enclosure. The state of the gas is described by specifying its pressure P, volume V and temperature T. If these parameters can be uniquely specified at a time, we say that the gas is in thermodynamic equilibrium. If we put the enclosure on a hot stove, the temperature of various parts of the gas is different and we cannot specify a unique temperature of the gas. The gas is not in thermodynamic equilibrium in such a case. |
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| Generally, the state of a system changes when we perform a process on a given system. The initial state of the system is described by the values P1, V1, T1 and the final state by P2, V2, T2. If the process is performed in such a way that at any instant during the process, the system is very nearly in thermodynamic equilibrium, the process is called quasi-static. This means, we can specify the parameters P, V, T uniquely at any instant during such a process. |
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| Actual processes are not quasi-static. To change the pressure of a gas, we can move a piston inside the enclosure. The gas near the piston is acted upon by greater force as compared to the gas away from the piston. The pressure of the gas may not be uniform everywhere while the piston is moving. However, we can move the piston very slowly to make the process as close to quasi-static as we wish. Thus, in a quasi-static process, all changes take place extremely slowly. |
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| A quasi-static process on a gas can be represented by a curve on a PV diagram (or a PT or a VT diagram). This is because, at any instant we have a unique value of P and a unique value of V. Suppose the curve in the above figure shows such a quasi-static process taking the system from an initial state i to a final state f. Let AB be an small, arbitrary part of this process. Suppose in this part, the gas takes an amount of heat DQ, from its surroundings and performs an amount of work DW, on the surroundings. It may be possible to design a reverse quasi-static process which takes the system from the state f to the state i, satisfying the following conditions: |
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| a) The reverse process is represented by the same curve as the direct process, with the arrow inverted. |
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| b) In the part BA, the system gives an amount of heat DQ to the surroundings and an amount of work W is performed on the system. |
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| If such a reverse process is possible, the original process is called a reversible process. In the direct process, the system has passed through certain equilibrium states in a sequence. When the process is reversed, the system passes through the same states in a reverse order and it returns the same amount of heat to the surroundings as was taken during the corresponding part in the direct process. Similarly, any work done by the system in the direct process is compensated by the equal work done on the system in the corresponding reverse process. |
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| A process is reversible if it satisfies two conditions. The process must be quasi-static and it should be non-dissipative. This means that there should be no friction, viscosity, etc. |
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| All processes described in this chapter and the following chapters will be assumed to be reversible unless stated otherwise. |
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| If the state of a system at the end of a process is the same as the state of the system at the beginning, the process is called a Cyclic process. If all parts of a cyclic process are reversible, it is a reversible cycle. |
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| Like pressure, volume, temperature and internal energy, we have another thermodynamic variable of a system, named entropy. In a given state of equilibrium, the system has a definite value of entropy. If the system has a temperature T (in absolute scale) and a small amount of heat DQ is given to it, we define the change in the entropy of the system as |
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| In general, the temperature of the system may change during a process. If the process is reversible, the change in entropy is defined as |
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| In an adiabatic reversible process, no heat is given out to the system. The entropy of the system remains constant in such a process. |
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| Entropy is related to the disorder in the system. Thus, if all the molecules in a given sample of a gas are made to move in the same direction with the same velocity, the entropy will be smaller than that in the actual situation in which the molecules move randomly in all directions. |
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| An interesting fact about entropy is that, it is not a conserved quantity. More interesting is the fact that entropy can be created but cannot be destroyed. The second law of thermodynamics may be stated in terms of entropy as follows: |
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| It is not possible to have a process in which the entropy of an isolated system decreases. |
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