Critical temperature

Why it matters in anaesthesia

Determines whether a substance can be liquefied by pressure at a given temperature; above this, only a supercritical fluid exists.
Explains storage behaviour of medical gases (e.g. why oxygen is stored as a compressed gas, whereas nitrous oxide is stored as a liquefied gas at room temperature).
Underpins cylinder pressure–content relationships and the interpretation of pressure gauges (especially for gases stored as liquids).
Links to vapour pressure, boiling point, and the need for temperature compensation in vapourisers (volatile agents have critical temperatures well above room temperature, enabling liquid phase).

Clinical examples

Nitrous oxide cylinder: contains liquid + vapour at room temperature; cylinder pressure reflects saturated vapour pressure until liquid is exhausted.
Oxygen cylinder: contains gas only at room temperature; pressure falls roughly in proportion to contents (at constant temperature).
CO2 cylinders (e.g. laparoscopic insufflation supply): stored as liquid + vapour at room temperature; similar gauge pitfalls to N2O.

Core definition and key concepts

Critical temperature (Tc): the highest temperature at which a substance can exist as a liquid; above Tc, no amount of pressure will produce a distinct liquid phase.
At Tc, the properties of liquid and vapour phases become identical; the phase boundary disappears.
Critical point: the unique combination of critical temperature (Tc) and critical pressure (Pc) at which the liquid–vapour equilibrium curve terminates.
Supercritical fluid: state above Tc (and above Pc) with properties intermediate between gas and liquid (high density like a liquid, diffusivity/viscosity more like a gas).

Phase behaviour (how to explain in a viva)

Below Tc: gas can be liquefied by increasing pressure at constant temperature (crossing the vapour–liquid coexistence line).
At Tc: latent heat of vaporisation tends to zero; surface tension tends to zero; meniscus disappears.
Above Tc: compression increases density smoothly without a phase change; no distinct boiling/condensation.
Practical implication: to store a substance as a liquid at ambient temperature, ambient temperature must be below Tc (and pressure must be sufficient).

Anaesthetic gases and agents: typical critical temperatures (order-of-magnitude knowledge)

Nitrous oxide: Tc ≈ 36.5 °C (close to room/body temperature) → readily exists as liquid in cylinders at room temperature under pressure.
Oxygen: Tc ≈ −118.6 °C → cannot be liquefied at room temperature by pressure; stored as compressed gas (or as cryogenic liquid in bulk systems).
Air/nitrogen: Tc well below 0 °C (nitrogen Tc ≈ −147 °C) → compressed gas storage at room temperature.
Carbon dioxide: Tc ≈ 31 °C → often stored as liquid + vapour at room temperature in cylinders.
Volatile agents (halothane, isoflurane, sevoflurane, desflurane): Tc far above room temperature → exist as liquids at room temperature; vapourisers deliver saturated vapour from liquid phase.

Cylinder pressure–content relationships (linking Tc to what you see on the gauge)

Gases stored as compressed gas (e.g. O2, air): at constant temperature, cylinder pressure is approximately proportional to the amount of gas remaining (ideal gas approximation).
Gases stored as liquid + vapour (e.g. N2O, CO2): cylinder pressure is determined mainly by saturated vapour pressure (temperature-dependent) and remains nearly constant while liquid remains.
When liquid is exhausted: pressure then falls rapidly with further use (now only gas phase).
Cooling during use: latent heat of vaporisation is taken from the cylinder contents/metal → temperature falls → saturated vapour pressure falls → gauge pressure drops even if significant liquid remains.

Related definitions often examined with Tc

Boiling point: temperature at which vapour pressure equals ambient pressure (e.g. 1 atm). Not the same as Tc; Tc is much higher than normal boiling point.
Vapour pressure: pressure exerted by vapour in equilibrium with its liquid at a given temperature; increases with temperature.
Critical pressure (Pc): minimum pressure required to liquefy a gas at Tc; above Tc, liquefaction impossible regardless of pressure.
Reduced temperature (Tr = T/Tc) and reduced pressure (Pr = P/Pc): used in corresponding states; real gases show similar behaviour at equal Tr and Pr.

How to draw/describe diagrams (common FRCA requirement)

P–T phase diagram: show solid–liquid line, liquid–vapour line ending at critical point, and triple point. Emphasise that the liquid–vapour boundary terminates at the critical point.
Isotherms on a P–V diagram (van der Waals): below Tc show a flat region (phase coexistence) after Maxwell construction; at Tc show an inflection point; above Tc show smooth curves without plateau.

Define critical temperature and explain its physical meaning.

A complete answer should include the definition, what happens to phases at Tc, and the implication for liquefaction by pressure.

Critical temperature (Tc) is the highest temperature at which a substance can exist as a liquid.
Above Tc, a gas cannot be liquefied by increasing pressure; compression produces a supercritical fluid without a phase boundary.
At Tc, liquid and vapour become indistinguishable: meniscus disappears; latent heat of vaporisation tends to zero.

What is the critical point? How does it relate to critical temperature and critical pressure?

Critical point is the end-point of the liquid–vapour equilibrium curve on a phase diagram.
It occurs at (Tc, Pc): the unique temperature and pressure where liquid and vapour phases become identical.
For T > Tc, no pressure can create a separate liquid phase; for T < Tc, liquefaction is possible if pressure is sufficiently high.

Nitrous oxide is stored as a liquid in cylinders at room temperature. Use critical temperature to explain why.

N2O has Tc ≈ 36.5 °C, which is above typical room temperature (~20 °C).
Because ambient temperature is below Tc, N2O can be liquefied by applying pressure; in a cylinder it exists as liquid + vapour at equilibrium.
Cylinder pressure is mainly the saturated vapour pressure at that temperature, so it stays relatively constant while liquid remains.

Oxygen is not stored as a liquid in standard cylinders at room temperature. Explain using critical temperature.

O2 has Tc ≈ −118.6 °C, far below room temperature.
At room temperature (>> Tc), oxygen cannot be liquefied by pressure alone; therefore standard cylinders contain compressed gas only.
Liquid oxygen is possible only at cryogenic temperatures (bulk storage), not by pressurising at ambient temperature.

A common FRCA question: Compare the cylinder pressure gauge behaviour of oxygen and nitrous oxide during use.

Structure your answer by storage state and what determines pressure.

Oxygen (compressed gas): pressure falls roughly proportionally with contents (assuming constant temperature).
Nitrous oxide (liquid + vapour): pressure remains near the saturated vapour pressure while liquid remains, then drops rapidly once liquid is exhausted.
During high flow, N2O cylinder cools (latent heat of vaporisation) causing a transient fall in pressure despite remaining liquid.

Explain what is meant by a supercritical fluid and how it relates to critical temperature.

A supercritical fluid exists when T > Tc (and typically P > Pc): there is no distinct liquid or gas phase.
It has liquid-like density with gas-like transport properties (diffusivity/viscosity), so it penetrates like a gas but dissolves substances like a liquid.
In anaesthesia, the concept mainly helps explain why some gases cannot be liquefied at ambient temperature and why phase boundaries disappear above Tc.

How would you describe the appearance of isotherms on a P–V diagram above and below the critical temperature?

Below Tc: isotherms show a region corresponding to two-phase coexistence (often depicted as a plateau after applying Maxwell construction).
At Tc: the isotherm has a point of inflection (first and second derivatives with respect to V are zero at the critical point in van der Waals model).
Above Tc: smooth monotonic curves with no plateau (no phase change on compression).

A past-style FRCA physics viva: Define boiling point and distinguish it from critical temperature.

Boiling point is the temperature at which vapour pressure equals ambient pressure (e.g. 1 atm for normal boiling point).
Critical temperature is the highest temperature at which a liquid phase can exist; above it, no phase boundary exists regardless of pressure.
A substance can have a normal boiling point far below Tc; Tc is not a boiling point at a particular pressure but a limit of phase coexistence.

Why does a nitrous oxide cylinder sometimes frost during use, and what does this do to the pressure gauge reading?

As N2O vaporises from liquid to replace gas drawn off, latent heat of vaporisation is absorbed from the cylinder contents and metal, cooling the cylinder.
Cooling reduces saturated vapour pressure, so the gauge pressure falls even though significant liquid may remain.
If cooling is marked, water vapour in air condenses/freezes on the cylinder surface (frost).

CO2 has a critical temperature around 31 °C. What practical implications does this have for CO2 cylinders used for laparoscopy?

At typical room temperature (< 31 °C), CO2 can exist as liquid + vapour in a cylinder under pressure, so gauge pressure may remain relatively constant while liquid remains.
During high flow, cooling can reduce cylinder pressure transiently (similar mechanism to N2O).
If ambient temperature approaches/exceeds Tc, behaviour moves towards supercritical; phase distinction reduces and simple ‘liquid present’ assumptions become less reliable.

Give a concise list of critical temperatures for common anaesthetic-related gases and state which are liquefiable at room temperature by pressure alone.

N2O Tc ≈ 36.5 °C → liquefiable at room temperature by pressure (room T < Tc).
CO2 Tc ≈ 31 °C → often liquefiable at room temperature by pressure (depends on ambient temperature).
O2 Tc ≈ −118.6 °C; N2 Tc ≈ −147 °C → not liquefiable at room temperature by pressure alone.

How does critical temperature relate to the design/operation of vapourisers for volatile agents?

Volatile agents have critical temperatures well above room temperature, so they exist as liquids in vapourisers at ambient conditions.
Vapouriser output depends on saturated vapour pressure of the liquid, which is temperature-dependent; hence temperature compensation is required.
Critical temperature is not the direct determinant of vapouriser output, but it explains why a stable liquid phase is available at room temperature.