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Answer the following questions based on the $P$ - $T$ phase diagram of carbon dioxide:
$(a)$ At what temperature and pressure can the solid, liquid and vapour phases of $CO _{2}$ co-exist in equilibrium?
$(b)$ What is the effect of decrease of pressure on the fusion and boiling point of $CO _{2} ?$
$(c)$ What are the critical temperature and pressure for $CO _{2} ?$ What is their sıgnificance ?
$(d)$ Is $CO _{2}$ solid, liquid or gas at $(a)\;-70\,^{\circ} C$ under $1\; atm$, $( b )\;-60\,^{\circ} C$ under $10 \;atm,$ $(c)$ $15\,^{\circ} C$ under $56$ atm ?
Solution
The $P-T$ phase diagram for $CO _{2}$ is shown in the following figure.
$C$ is the triple point of the $CO_2$ phase diagram. This means that at the temperature and pressure corresponding to this point (i.e., at $-56.6^{\circ} C$ and $5.11 atm$ ), the solid, liquid, and vaporous phases of $CO _{2}$ co-exist in equilibrium.
The fusion and boiling points of $CO _{2}$ decrease with a decrease in pressure.
The critical temperature and critical pressure of $CO _{2}$ are $31.1^{\circ} C$ and 73 atm respectively.
Even if it is compressed to a pressure greater than 73 atm, $CO _{2}$ will not liquefy above the critical temperature.
It can be concluded from the $P$ – $T$ phase diagram of $CO _{2}$ that:
$CO _{2}$ is gaseous at $-70^{\circ} C ,$ under $1$ atm pressure
$CO _{2}$ is solid at $-60^{\circ} C ,$ under $10$ atm pressure
$CO _{2}$ is liquid at $15^{\circ} C ,$ under $56$ atm pressure
