Stirring work

The shaft work done when a shaft turns a stirrer or paddle to agitate a liquid, as in system B of Fig. 3.10, is called stirring work. 

In system B, when the angular velocity co is zero and the water in which the stirrer is immersed is at rest, the torques Tsys and Tb are both zero. When co is finite and constant, the water is stirred in a turbulent manner and there is a Mctional drag force at the stirrer blades, as weU as Mctional forces at the shaft bearings. These forces make the value of Tsys have 

Because energy transferred to the system by dissipative work is converted to thermal energy, we could replace this work with an equal quantity of positive heat and produce the same overall change. The replacement of stirring work with heat was illustrated by experiment 3 on page 60. 

The shaft rotation angle d, which is the work coordinate for stirring work, is a property of the system but is not a state function, as we can see by the fact that the state of the system can be exactly the same for = 0 and = In. The work coordinate and work coefficient of work with a reversible limit are always state functions, whereas the work coordinate of any kind of dissipative work is not a state function. 

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Under conditions of adiabatic operation and negligible stirring work, both Q and Wr are zero, and the energy balance becomes... 

Another form of work is the shaft work indicated in Fig. 2.6 by rate Ws- In addition work may be associated with expansion or contraction of the control volume and there may be stirring work. These forms of work are all included in a rate term represented by W. The preceding equation may now be written ... 

A major concern with both pulse radiolysis and photolysis is that the radiation or light is capable of initiating undesirable side reactions. Stirring works... 

EtOH solution of sodium borohydride/ cone. HCl, RT, 1 h stirring work up... 

A good example of the quantitative measurement of stirring work is the set of experiments conducted by James Joule in the 1840s to determine the mechanical equivalent of heat. In effect, he determined the quantity of dissipative stirring work that could replace the heat needed for the same temperature increase. 

During a process with irreversible work, energy dissipation can be either partial or complete. Dissipative work, such as the stirring work and electrical heating described in previous sections, is irreversible work with complete energy dissipation. The final equilibrium state of an adiabatic process with dissipative work can also be reached by a path with positive heat and no work. This is a special case of the minimal work principle. 

Dissipative work is positive work with complete energy dissipation. In this type of work, the work coefficient vanishes in the limit of infinite slowness, and the work coordinate is not a state fimction. Examples are stirring work (Sec. 3.7.1) and the work of electrical heating (Sec. 3.8.2). 

A simple example will relate this rule to experience. We can increase the temperature of a liquid by allowing heat to flow reversibly into the liquid. It is impossible to duplicate this change of state by a reversible process without heat—that is, by using some kind of reversible work. The reason is that reversible work involves the change of a work coordinate that brings the system to a different final state. There is nothing in the rule that says we can t increase the temperature irreversibly without heat, as we can for instance with stirring work. 

To complete the setup, the sealed bomb vessel is immersed in a known mass of water in the calorimeter. A precision thermometer and a stirrer are also immersed in the water. With the stirrer turned on, the temperature is monitored until it is found to change at a slow, practically-constant rate. This drift is due to heat transfer through the jacket, mechanical stirring work, and the electrical work needed to measure the temperature. A particular time is chosen as the initial time t. The measured temperature at this time is Fi, assumed to be practically uniform throughout the system. 

The ignition work occvurs dvuing only a short time interval at the beginning of the proeess, and its value is known. The effects of heat transfer, stirring work, and temperature measurement continue throughout the covurse of the experiment. With these considerations, Eq. 11.5.6 becomes... 

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