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Thermal Properties of Matter

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Question : 16 of 22
Marks: +1, -0
Answer the following questions based on the P-T phase diagram of carbon dioxide :
(a) At what temperature and pressure can the solid, liquid and vapour phases of CO2\mathrm{CO}_2 co-exist in equilibrium?
(b) What is the effect of decrease of pressure on the fusion and boilingpoint of CO2\mathrm{CO}_2?
(c) What are the critical temperature and pressure for CO2\mathrm{CO}_2? What is theirsignificance?
(d) Is CO2\mathrm{CO}_2 solid, liquid or gas at (a) –70°C under 1 atm, (b) –60°C under 10atm, (c) 15°C under 56 atm?
Solution:  
(a) The solid, liquid and vapour phases of CO2\mathrm{CO}_2 can exist in equilibrium at its triple point O, corresponding to which
Ptr=5.11atmandTtr=56.6CP_{tr} = 5.11 \text{atm} \text{and} T_{tr} = -56.6^{\circ}\text{C}
(b) From the vaporisation curve (I) and the fusion curve (II), it follows that both the boiling and fusion points of CO2\mathrm{CO}_2 decrease with the decrease of pressure.
(c) For CO2,  Pc=73.0atmandTc=31.1C\mathrm{CO}_2,\; P_c = 73.0 \text{atm} \text{and} T_c = 31.1^{\circ}\text{C}
Above its critical temperature, CO2\mathrm{CO}_2 gas can not be liquified, however large pressure may be applied.
(d) (a) –70°C under 1 atm : This point lied in vapour region. Therefore, at–70°C under 1 atm, CO2\mathrm{CO}_2 is vapour.
(b) –60°C under 10 atm : this point lies in solid region. Therefore, CO2\mathrm{CO}_2 is solid at –60°C under 10 atm.
(c) 15°C under 56 atm : This point lies in liquid region. Therefore, CO2\mathrm{CO}_2 is liquid at 15°C under 56 atm.
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