An amount n (in moles) of a monatomic gas at initial temperature `T_(0)` is enclosed in a cylinderical vessel fitted with a ligth piston. The surrounding air has a temperature `T_(s)(gtT_(0))` . And the atmospheric pressure is `P_(a)` . Heat may be conducted between the surrounding and the gas through the bottom of the cylinder. The bottom has a surface area A, thickness x and thermal conductivity K. Assuming all change to be slow, find the distance moved by the piston in time t.