Joules Experiments

One can also do work by stirring, e.g. by driving a paddle wheel as in the Joule experiment above. If tire paddle is taken as part of the system, the energy input (as work) is detemiined by appropriate measurements on the electric motor, falling weights or whatever drives the paddle. 

A unit capable of producing higher energies was used for the 8- and 10-joule experiments. Gases produced by the flash and laser irradiations were analyzed by mass spectrometry after fractionation using the following baths liquid nitrogen, dry ice, ice water, water at room temperature, and water at 60° C. 

The concept behind the defining equation (Eq. (2.37)) comes from an experiment known as the Joule experiment, which is illustrated in Figure 2.3. The result of this experiment is known as the Joule effect. In this experiment the gas is confined in one part of a closed container and the other part is evacuated. The gas itself is taken to be the substance composing the system. However, the boundary between the system and its surroundings is chosen to be the walls of the container. The volume of the system is the total volume of the container and is not the same as the volume of the gas when it is... 

The expansion of an ideal gas in the Joule experiment will be used as a simple example. Consider a quantity of an ideal gas confined in a flask at a given temperature and pressure. This flask is connected through a valve to another flask, which is evacuated. The two flasks are surrounded by an adiabatic envelope and, because the walls of the flasks are rigid, the system is isolated. We now allow the gas to expand irreversibly into the evacuated flask. For an ideal gas the temperature remains the same. Thus, the expansion is isothermal as well as adiabatic. We can return the system to its original state by carrying out an isothermal reversible compression. Here we use a work reservoir to compress the gas and a heat reservoir to remove heat from the gas. As we have seen before, a quantity of heat equal to the work done on the gas must be transferred from the gas to the heat reservoir. In so doing, the value of the entropy function of the heat reservoir is increased. Consequently, the value of the entropy function of the gas increased during the adiabatic irreversible expansion of gas. 

The denominator on the right side of Eq. (4) is the heat capacity at constant pressure Cp. The numerator is zero for an ideal gas [see Eq. (1)]. Accordingly, for an ideal gas the Joule-Thomson coefficient is zero, and there should be no temperature difference across the porous plug. Eor a real gas, the Joule-Thomson coefficient is a measure of the quantity [which can be related thermodynamically to the quantity involved in the Joule experiment, Using the general thermodynamic relation ... 

The internal energy of a given mass of gas is independent of the volume occupied As a matter of fact (as shown by the porous plug experiment, which we will consider later), any actual gas only approximates to this statement There really was a very slight change m temperature in the bath in the Gay-Lussac-Joule experiment, though the methods employed were not sufficiently delicate to indicate it... 

This important formula1 does not by any means say that the work A must always be done when a gas expands lsothermally from the smaller volume to the larger volume 2 We have only need to call the Gay-Lussac or Joule experiment to mind (namely, the expansion of a gas into a vacuum) in order to see that the term A can be equal to zero... 

II The Joule Experiment and the Criterion of a Perfect Gas from, the standpoint of the two Laws of Thermodynamics... 

The entropy change for the irreversible Joule experiment may thus be calculated from the hypothetical, reversible process, because S is a function of state only. 

The derivative (dH/dp)j is very small for real gases, but can be measured. The Joule experiment, in which the gas expanded freely, failed to show a measurable difference in temperature between the initial and final states. Later, Joule and Thomson performed a different experiment, the Joule-Thomson experiment (Fig. 7.9). 

D2.5 In the Joule experiment, the change in internal energy of a gas at low pressures (a perfect gas) is zero. 

The quantity dT/dV)u is called the Joule coefficient. James Joule attempted to evaluate this quantity by measuring the temperature change accompanying the expansion of air into a vacuum—the Joule experiment. Write an expression for the total differential of U with T and V as independent variables, and by a procedure similar to that used in Sec. 7.5.2 show that the Joule coefficient is equal to... 

The Joule experiment was carried out several times with various volumes for the second chamber. The ratio AT/AV would be determined for each experiment and extrapolated to zero value of A V, where A V is the final volume of the gas minus its initial volume. This extrapolation is equivalent to taking the mathematical limit, so the result is a partial derivative, called the Joule coefficient and denoted by /uj ... 

There are better ways than the Joule experiment to determine values of (dU/dV)T,n, and we will discuss them in Chapter 4. Once values for Cy and for (dU/dV)r are obtained. All can be calculated for any process that begins with one equilibrium state... 

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