An ideal monatomic gas at 300 k expands adiabatically and reversibly to twice its volume. what is its final temperature?

In an adiabatic process, the following relationship holds:

where T is the gas temperature, V is the volume and  is the adiabatic index, which is equal to  for a monoatomic gas.

We can re-write the equation as

where the labels 1,2 refer to the initial and final conditions of the gas.
Let's rewrite it for , the final temperature:


We can now substitute the initial temperature, T1=300 K, and , because the final volume is twice the initial one. So we find the value of the final temperature:

An  atom  (ours, not carroll's) consists of a positively charged  nucleus, surrounded by one or more negatively charged particles called  electrons. the positive charges equal the negative charges, so the atom has no overall charge; it is electrically neutral. most of an atom's mass is in its nucleus; the mass of an electron is only 1/1836 the mass of the lightest nucleus, that of hydrogen. although the nucleus is heavy, it is quite small compared with the overall size of an atom. the radius of a typical atom is around 0.1 to 0.25 nanometres (nm), whereas the radius of a nucleus is about 10-6  nm.  *  if an atom were enlarged to the size of the earth, its nucleus would be only 200 feet in diameter and could easily rest inside a small football stadium.read more on -