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Q11.22(d):
Answer the following questions based on the P – T phase diagram of $CO_2$: (d) $CO_2$ is heated to a temperature 70 °C and compressed isothermally. What changes in its properties do you expect to observe ?
Solution :
Step 1: Analyzing the Critical Parameters of $CO_2$
To determine the state changes of carbon dioxide ($CO_2$) at $70\text{ }^\circ\text{C}$, we must first identify the critical temperature ($T_c$) of the substance.
- Critical Temperature of $CO_2$ ($T_c$): $31.1\text{ }^\circ\text{C}$
- Critical Pressure of $CO_2$ ($P_c$): $73.8\text{ atm}$
- Operating Temperature ($T$): $70\text{ }^\circ\text{C}$
Step 2: Thermodynamic Behavior Analysis
Since the given temperature ($70\text{ }^\circ\text{C}$) is greater than the critical temperature ($31.1\text{ }^\circ\text{C}$), $CO_2$ exists in the gaseous phase (specifically as a supercritical fluid if pressure is increased sufficiently).
As the gas is compressed isothermally at $70\text{ }^\circ\text{C}$:
- The volume of the $CO_2$ sample decreases, adhering to Boyle's Law ($PV = \text{constant}$) for ideal gases, though it will show deviations as a real gas.
- The density of the fluid increases continuously.
- There is no sharp transition or phase change (i.e., no condensation into a distinct liquid phase).
- The substance transitions from a gaseous state to a dense, supercritical fluid state.
Step 3: Comparison of Physical Properties
| Property | Observation at $T > T_c$ |
|---|---|
| Phase Transition | None (remains a fluid) |
| Density | Increases monotonically |
| Appearance | Uniform; no meniscus formation |
Summary of Observations
Because the temperature $70\text{ }^\circ\text{C} > 31.1\text{ }^\circ\text{C}$, the $CO_2$ will not liquefy. As it is compressed, it will undergo a continuous transition into a dense, supercritical state. The substance will retain the properties of a fluid, exhibiting high density, but will not undergo a phase separation into liquid and vapor phases typically associated with condensation.
Final Solution: $CO_2$ will not liquefy; it will exist as a gas that becomes increasingly dense and eventually enters a supercritical fluid state without any discontinuous change in state.
More Questions from Class 11 Physics Thermal Properties of Matter ADDITIONAL EXERCISES
- Q11.21(a): 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 $CO_2$ co-exist in equilibrium ?
- Q11.21(b): Answer the following questions based on the P-T phase diagram of carbon dioxide: (b) What is the effect of decrease of pressure on the fusion and boiling point of $CO_2$ ?
- Q11.21(c): Answer the following questions based on the P-T phase diagram of carbon dioxide: (c) What are the critical temperature and pressure for $CO_2$ ? What is their significance ?
- Q11.21(d): Answer the following questions based on the P-T phase diagram of carbon dioxide: (d) Is $CO_2$ solid, liquid or gas at (a) –70 °C under 1 atm, (b) –60 °C under 10 atm, (c) 15 °C under 56 atm ?
- Q11.22(a): Answer the following questions based on the P – T phase diagram of $CO_2$: (a) $CO_2$ at 1 atm pressure and temperature – 60 °C is compressed isothermally. Does it go through a liquid phase ?
- Q11.22(b): Answer the following questions based on the P – T phase diagram of $CO_2$: (b) What happens when $CO_2$ at 4 atm pressure is cooled from room temperature at constant pressure ?
- Q11.22(c): Answer the following questions based on the P – T phase diagram of $CO_2$: (c) Describe qualitatively the changes in a given mass of solid $CO_2$ at 10 atm pressure and temperature –65 °C as it is heated up to room temperature at constant pressure.
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