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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 ?
Solution :
Initial State & Physical Context
The phase diagram of $CO_2$ (Carbon Dioxide) maps the state of matter as a function of Pressure ($P$) and Temperature ($T$). Key reference points for $CO_2$ include:
- Triple Point: $P_t = 5.11 \text{ atm}$, $T_t = 216.55 \text{ K}$ ($-56.6 ^\circ\text{C}$).
- Critical Point: $P_c = 73 \text{ atm}$, $T_c = 304.15 \text{ K}$ ($31.1 ^\circ\text{C}$).
Given the condition: $P = 4 \text{ atm}$ (Constant). Since $4 \text{ atm} < 5.11 \text{ atm}$ (the triple point pressure), $CO_2$ does not possess a liquid phase at this pressure.
Step 1: Visualization of the P-T Phase Path
Step 2: Thermodynamic Analysis of the Cooling Process
The cooling process starts at room temperature ($T \approx 293 \text{ K}$) at a constant pressure of $4 \text{ atm}$.
- Initial Phase: At $4 \text{ atm}$ and room temperature, $CO_2$ exists in the gaseous (vapor) phase.
- The Phase Boundary: As the temperature decreases, the state moves horizontally to the left on the phase diagram. Because the pressure is constant at $4 \text{ atm}$, the system will intersect the sublimation curve (the boundary separating the solid phase and the vapor phase).
- The Phase Transition: Since the triple point pressure for $CO_2$ is $5.11 \text{ atm}$, and our operating pressure is below this, the liquid phase is skipped entirely [Per the Phase Rule: $F = C - P + 2$]. The $CO_2$ undergoes desublimation (or deposition).
Step 3: Conclusion on the Physical Outcome
When the temperature drops to the sublimation temperature corresponding to $4 \text{ atm}$, the gaseous $CO_2$ molecules transition directly into the solid state without passing through the liquid state. This solid $CO_2$ is commonly referred to as "dry ice."
Final Solution: The $CO_2$ will condense directly from the gaseous phase to the solid phase (dry ice) at the sublimation temperature, as the given pressure of $4 \text{ atm}$ is lower than the triple point pressure of $5.11 \text{ atm}$.
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(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.
- 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 ?
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