A cylinder containing molecular oxygen O₂, a volume equal to 16.4 liters and pressure of 300 atmospheres, is in thermal equilibrium with the environment at 27 °C, given the universal gas constant \( R=0.082\;\frac{\text{atm.}\ell}{\text{mol.K}} \) and considering oxygen as an ideal gas, determine:
a) The number of gas moles in the cylinder;
b) The mass of the gas in the cylinder, the molar mass of the oxygen M = 16 g/mol;
c) The volume of the gas if it were the pressure of 1 atm.

A gas initially occupies a volume of 15 liters at 27 °C and exerts a pressure of 5 atmospheres on the walls of the container where it is closed. Determine:
a) The volume occupied by the gas at 127 °C under the pressure of 5 atmospheres;
b) From the initial state, the pressure exerted by the gas at 27 °C when its volume increases to 30 liters;
c) From the initial state, the temperature of the gas, under a pressure of 8 atmospheres and 15 liter volume.

A gas is initially at a pressure of 2 atmospheres, volume of 4 liters, and temperature of 300 kelvins. From this state, the pressure increases at a constant volume up to a pressure of 5 atmospheres, determine its temperature at the end of this process. After this first process, the gas expanded at a constant temperature to a volume of 8 liters, determine its pressure at the end of this second process. From this state, the gas is heated at a constant pressure to a temperature of 900 kelvins, determine the final volume of the gas. Plot the gas processes in a graph of the pressure as a function of volume p×V.