Solution:

Cascade Process - Liquefaction of oxygen:

• The critical temperatures for oxygen -119°C and critical pressure is 49.7 atm.

• Principle:

• When a liquid is allowed to evaporate under reduced pressure, it produces high cooling.

• The apparatus arrangement used in this process is shown in the figure.

• It consists of three narrow tubes. A,B and C enclosed by three outer jackets P, Q and R respectively.

• The narrow tubes and the outer jackets are linked with the compression pumps P1 , P2 and P3 as shown in the figure.

• The methyl chloride gas of critical temperature 145° C is compressed by the pump P1 through the tube A. It is cooled by the cold water circulating in the jacket P.

• Here the methyl chloride reaches the temperature lower than its critical temperature. Then it is liquefied under high pressure. The liquid methyl chloride is collected in the jacket Q and evaporates under reduced pressure lowering the temperature to -90° C.

• The ethylene gas of critical temperature 10° C is compressed by the pump P2 through the tube B. It is cooled to -90° C by liquid methyl chloride.

• Then it is liquefied under high pressure. The liquid ethylene is collected in the jacket R and evaporates under reduced pressure lowering the temperature to -160° C.

• The oxygen gas of critical temperature - 119° C is compressed to 50 atmospheric pressure by the pump P3 and passed through the tube C. It is cooled to - 160° C by liquid ethylene in R. Then it is liquefied and the liquid oxygen is collected in the Dewar flask D.

Disadvantage:

• The lowest temperature obtained in this process is -160° C. Therefore the cascade process cannot be used to liquefy hydrogen and helium whose critical temperatures are lower than - 160° C.