The critical temperature and the critical pressure of a gas are `T_(c) and P_(c)`, respectively. If the gas exists at a temperature of T and a pressure P, then under which of the following conditions will the gas not be liquefied?
(i) `T gt T_(c) , P gt P_(c)`
(ii) `T=T_(c),PgtP_(c)`
(iii) `T=T_(c),PltP_(c)`
(iv) `T lt T_(c),P=P_(c)`

Explanation

(i) Under the conditions of `T gt T_(c) and P gt P_(c)`, the gas cannot be liquefied because its temperature is above its critical temperature.
(ii) Under the conditions of `T=T_(c) and P gt P_(c)`, it is possible to liquefy the gas. Because the gas is at its critical temperature and its pressure is above critical pressure.
(iii) Under the conditions of `T=T_(c) and P lt P_(c)`, it is not possible to liquefy the gas as the minimum pressure needed to liquefy a gas at its critical temperature most be equal to `P_(c)` to greater than `P_(c)`.
(iv) Under the conditions of `T lt T_(c) and P=P_(c)`, the gas can be liquefied. because the gas is below its critical temperature and the pressure of the gas is equal to its critical pressure, the minimum pressure required to liquefy a gas at its critical temperature.