Cooling by Adiabatic Expansion

Definition: The cooling produced when a compressed gas expands under adiabatic conditions is called cooling by adiabatic expansion.

Adiabatic Relation

For a reversible adiabatic expansion of an ideal gas,

\[ PV^\gamma=\text{constant} \]

where

\[ \gamma=\frac{C_P}{C_V} \]

Using the ideal-gas equation, the temperature-pressure relation becomes

\[ TP^{(1-\gamma)/\gamma}=\text{constant} \]

Therefore, between two states,

\[ \boxed{ \frac{T_2}{T_1} = \left( \frac{P_2}{P_1} \right)^{(\gamma-1)/\gamma} } \]

Hence,

\[ \boxed{ T_2 = T_1 \left( \frac{P_2}{P_1} \right)^{(\gamma-1)/\gamma} } \]

Thus, according to the ideal-gas adiabatic relation, the temperature decreases considerably during expansion.

Liquefaction by Adiabatic Expansion

Linde Air Liquefier

The Linde air liquefier operates primarily on the principles of regenerative cooling and Joule–Thomson expansion.

Atmospheric air is first purified and dried. Water vapour and carbon dioxide are removed using suitable absorbents such as calcium chloride, caustic potash and phosphorus pentoxide.

Working

The purified air is compressed to a high pressure and passed through a cooling system. It then enters a heat exchanger and reaches a throttle valve.

At the throttle valve, the compressed air undergoes Joule–Thomson expansion to a lower pressure. The resulting temperature decrease is initially small.

The cold expanded gas then returns through the heat exchanger. During this return flow, it cools the incoming high-pressure air.

The precooled air again undergoes expansion, producing further cooling. The process is repeated continuously.

Eventually, the temperature becomes sufficiently low for air to liquefy. The liquid air is collected in a Dewar flask.

Purification → Compression → Heat Exchange → Expansion → Regenerative Cooling → Liquefaction

Dewar Hydrogen Liquefier

Hydrogen is more difficult to liquefy than many other gases because its Joule–Thomson inversion temperature is very low. Hydrogen must first be cooled below its inversion temperature before Joule–Thomson expansion can produce further cooling.

Liquid air is therefore used for preliminary cooling of hydrogen.

Working

Pure hydrogen is first cooled and then passed through regenerative coils. The incoming hydrogen is cooled by the returning cold hydrogen produced during expansion.

The hydrogen passes successively through different cooling stages. Liquid air provides the initial precooling, while regenerative heat exchange provides additional cooling.

After sufficient precooling, hydrogen is expanded through a throttle valve. The resulting temperature decrease further reduces the temperature of the system.

The process is repeated until the hydrogen reaches its liquefaction temperature. The resulting liquid hydrogen is collected in a Dewar vessel.

Purification → Compression → Precooling → Regenerative Heat Exchange → Expansion → Further Cooling → Liquid Hydrogen