Pressure-volume work Word done

Professor Nicolas L. S. Carnot, in the late nineteenth century, realized that the area inside the plot of pressure vs. volume represented the work needed to compress gas in a reciprocating compressor. In other words, the change of pressure, multiplied by the change in volume, is equal to the work done by the piston on the gas. Professor Carnot called this PV (pressure vs. volume) work. He then used calculus to sum up the area inside the lines shown in Fig. 29.2. The total area is now called ideal compression work. 

Since the gas expands into a vacuum, that is, against no external pressure, the work of expansion W is also zero. It follows, therefore, from equation (7.2), that AE must be zero in the process in other words, there is no change in the energy content of an ideal gas os a result of free expansion, i.e., a volume increase in which no external work is done. The energy of the gas depends on two variables, e.g., volume and temperature hence, the conclusion just reached may be represented mathematically in the form... 

In other words, the work done by the substance when its volume increases by a small amount is equal to the pressure of the substance multiplied by its increase in volume. It should be noted that dW=p dV is equal to the shaded area in the graph shown in Figure 2.1 that is, it is equal to the area under the curve PQ. When the substance passes from state A with volume Vj to state B with volume V2 (Fig. 2.1), during which its pressure p changes, the work W done by the substance is equal to the area under the curve AB. That is. 

When considering gas systems, the amount of work done by the gas is, of course, also path dependent. In other words, it depends on how you change the state parameters such as the volume, pressure, and/or temperature. 

In other words, if the gaseous HC1 simply dissolved without volume change, the heat released by the process (75.3 kJ) would cause the system s internal energy to diminish by 75.3 kJ. But the volume decrease due to the disappearance of the gas is equivalent to compression of the system by the pressure of the atmosphere the resulting work done on the system acts to increase its internal energy, so the net value of AU is -72.82 kJ instead of -75.3 kJ. 

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