For the isothermal expansion of a gas into a vacuum, \(\Delta E\) = 0, q = 0, and w = 0.
(a) Is this a spontaneous process?
(b) Explain why no work is done by the system during this process.
(c) What is the “driving force” for the expansion of the gas: enthalpy or entropy?
Step 1 of 5) Other isotopes can be similarly used to date other types of objects. For example, it takes 4.5 * 109 yr for half of a sample of uranium-238 to decay to lead-206. The age of rocks containing uranium can therefore be determined by measuring the ratio of lead-206 to uranium-238. If the lead-206 had somehow become incorporated into the rock by normal chemical processes instead of by radioactive decay, the rock would also contain large amounts of the more abundant isotope lead-208. In the absence of large amounts of this “geonormal” isotope of lead, it is assumed that all of the lead-206 was at one time uranium-238. The oldest rocks found on Earth are approximately 3 x 109 yr old. This age indicates that Earth’s crust has been solid for at least this length of time. Scientists estimate that it required 1 x 109 to 1.5 x 109 yr for Earth to cool and its surface to become solid, making the age of Earth 4.0 to 4.5 * 109 yr.