Linde's Method of Liquefaction of Gases
Linde's method is based on the principle known as Joule-Thomson effect. According to this principle, when a gas under high pressure is allowed to expand into a region of low pressure, its temperature falls. The gas does not do any external work but the kinetic energy and hence, the temperature of the gas is lowered because of the work done in separating the molecules against their attractive intermolecular forces. A precaution is required in this process. To have a cooling effect, a gas is to be brought below a characteristic temperature, known as inversion temperature, before allowing it to expand. If the temperature of the gas is above its inversion temperature, Joule-Thomson expansion results in heating. A schematic diagram of the equipment used in Linde's method is shown below.
The gas at a temperature lower than its inversion temperature is compressed using a compressor. This gas is then allowed to expand through a valve which, results in its cooling. The cold gas is used in cooling the high pressure gas in the heat exchanger and is recirculated through the compressor. It gets cooled still further, as it expands. The cycle continues till the liquefied gas drops from the throttle.
2. Essential Conditions
For Linde's method to work, the gas must be below its Inversion Temperature ($T_i$) before expansion. If a gas is expanded above this temperature, it will actually heat up instead of cooling down.
The cooling produced is defined by the Joule-Thomson coefficient ($\mu_{JT}$):
$$\mu_{JT} = \left( \frac{\partial T}{\partial P} \right)_H$$
3. Limitations
Linde's method is relatively inefficient because it relies purely on internal work (overcoming intermolecular forces). Modern industrial plants often use the Claude Process, which incorporates an expansion engine to perform external work, resulting in faster cooling.