An isotherm is a line of constant temperature
Compressed gases in a cylinder can either stay as a gas, or change state to form a liquid due to the higher pressure (both carbon dioxide and nitrous oxide do this).
A graph of pressure against time for nitrous oxide is shown below. The isothermal lines are shown for 40°C, 36.6°C and 20°C.
At 40°C, nitrous oxide is above its critical temperature and so it is a gas no matter whatever pressure is being applied.
When it is compressed (moving from right to left along the isotherm) the pressure increases smoothly. At 36.6°C (the critical temperature), as soon as the pressure reaches the critical pressure (72 bar), the gas becomes a liquid.
At 20°C, once the pressure reaches 52 bar (the saturated vapour pressure of nitrous oxide at 20°C), some of the gas condenses so that liquid and vapour are both present. Further decreases in volume cause more vapour to condense, with no associated rise in pressure. When all the vapour has condensed to a liquid, any further reduction in volume causes a rapid rise in pressure.
In most circumstances, nitrous oxide is stored below its critical temperature of 36.4 C. It therefore exists in the cylinder as a vapour in equilibrium with the liquid below it.
To determine how much nitrous oxide remains in a given cylinder, it must be weighed, and the weight of the empty cylinder, known as the tare weight, subtracted. Using Avogadro’ s law, the number of moles of nitrous oxide may now be calculated. V/n= K, where V = volume of gas, n = amount of substance of the gas, K = a proportionality constant
Using the universal gas equation, the remaining volume can be calculated. PV = nRT, where P = pressure, V = volume, n = the number of moles of the gas, R = the universal gas constant (8.31 J/K/mol), T = temperature
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