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:
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 AB➠ only 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.