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 obtained by him in both gaseous and liquid states.

Results of Andrew’s experiment in Graphical form:

Andrew's Experiment and Isotherms of Carbon dioxide

Fig: Isotherms of \(C{O}_2\) at different temperatures

Note: In each of these graphs, the volume is plotted against pressure at a constant temperature.

P-V Isotherm at 13.1°C (286.1K)
It consists of three parts i.e., curve AB, horizontal portion BC and vertical curve CD
1. Along ABonly gaseous \(C{O}_2\) exists.
2. Along BC liquid \(C{O}_2\) exists in equilibrium with its vapour form.
3. Along CD only liquid \(C{O}_2\) exists.

At point A, gaseous \(C{O}_2\) exists at low pressure.
• As pressure is increased, the volume decreases along curve AB.
Thus curve AB represents the compression of \(C{O}_2\) gas.

At point B, the liquification starts and the volume decreases suddenly.
• Now, along  horizontal portion BC of the isotherm, the liquification of gas continues while the pressure held constant.

At point C, all the gaseous \(C{O}_2\) is converted into liquid state.
• The vertical curve CD of the isotherm is the P-V curve of the liquid \(C{O}_2\).
• This curve represents that, on increasing the pressure, there is a small change in the volume.
As the CD is almost vertical, i.e., the liquid \(C{O}_2\) is not compressible.

P-V isotherm at 21.5°C
Along EF, \(C{O}_2\) exists as gas.

At point F, liquefaction starts.
Along FG, both gaseous and liquid \(C{O}_2\) are present and the pressure of the system remains almost same.

At point G, all the gas has been condensed and
Along steep line GH, the application of pressure results merely in compression of the liquid.

Note :
Isotherm EFGH at 21.5°C is similar to those of ABCD. Only difference is that the horizontal portion FG of the isotherm is small than that of CD.
• As the temperature is increased, the horizontal portion of the isotherms becomes smaller and smaller until at 31.1°C and it reduces to a point at X

P-V isotherm at 31.1°C

At 31.1°C, \(C{O}_2\) remains gaseous only up to a pressure of 72.7 atm.
i.e., the portion IX of the isotherm represents the P-V curve of \(C{O}_2\) gas.

At 72.7 atm (point X), there is first appearance of liquid \(C{O}_2\).
Since 31.1°C is the highest temperature at which the liquid is observed firstly,
i.e., 31.1°C must be the critical temperature (\(T_{C}\)) of the \(C{O}_2\)
Further increase in the pressure at 31.1°C shows only the presence of liquid \(C{O}_2\) .

Andrew concluded that, if the temperature of \(C{O}_2\) is above 31.1°C , then it cannot be liquefied even at high pressures.

Other Important Points:

  • At point X, the boundary between the liquid and gaseous phase disappears.
  • At point X, the gas and liquid have same density and are indistinguishable.
  • As above 31.1°C, there is no indication of liquefaction. Since it is the temperature above which a gas cannot be liquefied i.e., the critical temperature (\(T_{C}\)) of \(C{O}_2\)
  • The point X represents \(C{O}_2\) in its critical state and the corresponding pressure (72.7 atm) is called the critical pressure of \(C{O}_2\)
  • Above 31.1°C , the isotherms are very similar to the hyperbolic plots demanded by Boyle’s law and shows no presence of liquid \(C{O}_2\) even at highest pressure so applied.
  • Temporary gases like CO2, Cl2, NH3 etc.have \(T_{C}\) well within the range of ordinary temperatures.
  • Permanent gases like H2, N2, O2 etc. have very low \(T_{C}\) much below the room temperature.

Leave a Comment

WhatsApp
error: Content is protected !!