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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 $CO_2$ ?
Solution :
Theoretical Foundation: Phase Diagram of $CO_2$
The phase diagram of $CO_2$ (Pressure-Temperature) represents the equilibrium states of the substance. Unlike water, $CO_2$ exhibits a positive slope for the fusion (melting) curve, meaning the solid phase is denser than the liquid phase [Per the Clausius-Clapeyron relation: $\frac{dP}{dT} = \frac{L}{T(V_v - V_l)}$].
Step 1: Analyzing the Fusion Point (Solid-Liquid Equilibrium)
The fusion curve for $CO_2$ starts from the triple point ($5.11 \text{ atm}$, $216.55 \text{ K}$) and slopes upward to the right.
- The slope of the fusion line is positive, signifying that as pressure increases, the melting point increases.
- Conversely, a decrease in pressure results in a decrease in the fusion point (melting temperature).
Step 2: Analyzing the Boiling Point (Liquid-Vapor Equilibrium)
The vaporization curve extends from the triple point to the critical point ($73 \text{ atm}$, $304.15 \text{ K}$).
- As pressure decreases along the vaporization curve, the boiling point moves toward lower temperatures.
- A decrease in pressure leads to a decrease in the boiling point of the liquid phase.
Visual Representation of $P-T$ Phase Diagram ($CO_2$)
Summary of Thermodynamic Effects
| Phase Change | Effect of Pressure Decrease | Thermodynamic Principle |
|---|---|---|
| Fusion | Decreases | Positive Clausius-Clapeyron Slope |
| Boiling | Decreases | Standard Volumetric Expansion ($V_v > V_l$) |
Final Solution: For carbon dioxide, a decrease in pressure results in a decrease in both the fusion point (melting temperature) and the boiling point.
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(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.
- 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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