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:
“To give an accurate description of what has never occurred is not merely the proper occupation of the historian, but the inalienable privilege of any man of parts and culture.”
—Oscar Wilde (1854–1900)
“The Sage of Toronto ... spent several decades marveling at the numerous freedoms created by a “global village” instantly and effortlessly accessible to all. Villages, unlike towns, have always been ruled by conformism, isolation, petty surveillance, boredom and repetitive malicious gossip about the same families. Which is a precise enough description of the global spectacle’s present vulgarity.”
—Guy Debord (b. 1931)
“An intentional object is given by a word or a phrase which gives a description under which.”
—Gertrude Elizabeth Margaret Anscombe (b. 1919)