Description
We consider n moles of an ideal gas at pressure Pi and temperature Ti, confined to the left-hand side (as drawn) of a thermally-isolated container, that occupies a volume Vi = V0. The right-hand side of the container, also with volume V0, is evacuated. The tap (solid line) between the two halves of the container is then suddenly opened and the gas fills the entire container of volume Vf = 2V0. We propose that both the previous and new temperature and pressure (Tf, Pf) follow the Ideal Gas Law, so that initially we have PiVi = nRTi and then, when the tap is opened, we have PfVf = nRTf, where R is the molar ideal gas constant.
As the system is thermally isolated, it cannot exchange heat with its surroundings. Also, since the system's volume is kept constant, the system does not do work on its surroundings. As a result, the change in internal energy ΔU = 0, and because U is a function of temperature only for the ideal gas, we know that Ti = Tf. This implies that PiV0 = Pf(2V0), and thus the pressure halves; i.e. Pf = ½Pi.
Read more about this topic: Joule Expansion
Famous quotes containing the word description:
“God damnit, why must all those journalists be such sticklers for detail? Why, they’d hold you to an accurate description of the first time you ever made love, expecting you to remember the color of the room and the shape of the windows.”
—Lyndon Baines Johnson (1908–1973)
“Once a child has demonstrated his capacity for independent functioning in any area, his lapses into dependent behavior, even though temporary, make the mother feel that she is being taken advantage of....What only yesterday was a description of the child’s stage in life has become an indictment, a judgment.”
—Elaine Heffner (20th century)
“The next Augustan age will dawn on the other side of the Atlantic. There will, perhaps, be a Thucydides at Boston, a Xenophon at New York, and, in time, a Virgil at Mexico, and a Newton at Peru. At last, some curious traveller from Lima will visit England and give a description of the ruins of St. Paul’s, like the editions of Balbec and Palmyra.”
—Horace Walpole (1717–1797)