Critical Phenomenon - educontenthub

Liquefaction of gases

liquefaction of gases For liquefaction of gases having fairly high critical temperature e.g. ammonia, chlorine, sulphur dioxide and carbon dioxide, the application of a suitable pressure alone is sufficient. For liquefaction of permanent gases which have very low critical temperature e.g. hydrogen, oxygen, nitrogen, helium etc. application of pressure alone will not bring liquefaction but … Read more

The Law of Corresponding States

The Law of Corresponding States In 1881, van der Waals showed that if pressure, volume and temperature of a gas are expressed in terms of its critical pressure, critical volume and critical temperature, then we can obtain an important generalization, viz., known as the law (principle) of corresponding states. The Law of corresponding states can … Read more

Critical Compressibility Factor

Critical Compressibility Factor ( ${Z}_c$ ) The critical Compressibility factor ${Z}_c$ of a van der Walls gas is given by, ${Z}_c=\frac{{P}_c{V}_c}{R{T}_c}$ (1) As we know, ${P}_c=\frac{a}{27{b}^2}$ ${V}_c=3b$ ${T}_c=\frac{8a}{27Rb}$ By putting the value of ${P}_c, {V}_c$ and ${T}_c$ in equation 1 : $\Rightarrow{Z}_c=\frac{(\frac{a}{27{b}^2})(3b)}{{R}[\frac{8a}{27Rb}]}$ $\Rightarrow{{Z}_c=\frac{3}{8}}$ $\Rightarrow\fbox{${Z}_c$=0.375}$ Note- We can test whether a gas behaves as a van der Waals gas … Read more

Relationship Between Critical Constants And Vander Waal’s Constants

Relationship Between Critical Constants And Vander Waal’s Constants Vanderwaals equation for one mole of gas is, $\left( {P + \frac{{a}}{{V^2 }}} \right)\left( {V – n} \right) = RT$ $PV+\frac{a}{V}-Pb-\frac{ab}{V^2}=RT$ Multiplying both sides by $\frac{V^2}{P}$ and arranging the obtained equation in decreasing powers of V, we get $V^3-(b+\frac{RT}{P})V^2 +\frac{aV}{P} -\frac{ab}{P}=0\tag1\\$ viz., a cubic equation … Read more

The Isotherms of van der Wall’s Equation

The Isotherms of van der Wall’s Equation As we know, the Vanderwaals equation for one mole of gas is, $\left( {P + \frac{{a}}{{V^2 }}} \right)\left( {V – b} \right) = RT$ ⇒ $PV+\frac{a}{V}-Pb-\frac{ab}{V^2}=RT$ Multiplying both sides by $\frac{V^2}{P}$ and arranging the obtained equation in decreasing powers of V, we get $\fbox{$V^3-(b+\frac{RT}{P})V^2 +\frac{aV}{P} -\frac{ab}{P}=0$}$ viz., … Read more

Continuity of State

CONTINUITY OF STATE At the critical temperature, the gaseous $C{O}_2$ cannot be distinguished from liquid carbon dioxide which indicates that the conversion of $C{O}_2$ gas into liquid $C{O}_2$ or vice versa is not a sharp or discontinuous process but is a continuous process. As shown in the figure, if the ends of the horizontal portions … Read more

PV ISOTHERM OF REAL GASES

PV ISOTHERM OF REAL GASES The plots of pressure vs volume at a given temperature of real gases are called P-V isotherms In 1869, Thomas Andrews studied the critical phenomenon in detail. He measured the variation of volume of $C{O}_2$ with pressure at different temperatures. The first complete data on P-V isotherms of $C{O}_2$ was … Read more

Critical Temperature Critical Pressure Critical Volume and their Determination

Critical Temperature Critical Pressure Critical Volume and their Determination THE CRITICAL PHENOMENON • According to kinetic theory of gases, the gas molecules are constantly moving. ∴ the gas molecules possess kinetic energy. • average kinetic energy of the molecules is directly proportional to the absolute temperature. • Average K.E $\propto$ absolute temperature. i.e., As the temperature decreases, the kinetic … Read more