Figure 2.1 Cylinder with frictionless piston.
because p is constant. It follows that v (
The ratio of the two specific heats is _cp _ R(1 + v/2)
R J K_1kmole
2.9 Adiabatic Processes
In the closed system we have considered so far, we described the interplay between the internal energy, U, the work, W, and the heat, Q. The simplest possible system is one in which the cylinder is so well insulated that heat can neither enter nor leave. In such an adiabatic system, AQ = 0. As the piston moves down, the work done on it is entirely transformed into an increase in internal energy: AU = W. The compression can be accomplished in a gradual manner so that at any given instant the pressure exerted by the piston is only infinitesimally larger than that of the gas—the compression is a succession of quasi-equilibrium states, and the pressure is always uniform throughout the gas. Such is the case, for instance, when the piston is pressed down by the connecting rod of a mechanical heat engine, even though the action may appear to be very rapid. It is also possible to compress a gas abruptly as when an immobilized piston loaded with a heavy weight is suddenly released. In this case, the pressure of the gas immediately under the piston will rise rapidly, but there is no time to transmit this change to the rest of the gas. A nonequilibrium situation is created. The former case—gradual compression—is by far the most common and most important. Nevertheless, we will first consider the abrupt compression because gradual compression can be treated as an infinite succession of infinitely small abrupt steps.
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