The diagram shown below is a theoretical representation of the phase diagram for carbon. The hatched regions indicate conditions under which the phase is predicted to be metastable— in effect this means that multiple phases can co-exist in these regions. Using this diagram, answer the following questions concerning the phases of carbon. Note the indicated scales for the horizontal and vertical axes (1 bar = 0.0001 GPa). 1000T 100- p/GPa 10 0.1- 0.01 0.001+ i diamond graphite T 2 liquid vapor 4 5 6 7 8 9 10 T/1000 K (a) Does graphite melt or sublime at 10 bars of pressure? (b) If pressure remains constant, what are the possible phase transitions for diamond at 4500 K as T is increased? (c) Identify the approximate temperature and pressure of the standard solid-liquid-gas triple point on this diagram. Are there other triple points indicated in the diagram? (d) Estimate the maximum temperature at which graphite can exist at P = 1 GPa. What would happen if the pressure is increased for a sample of graphite at this temperature?

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The diagram shown below is a theoretical representation of the phase diagram for carbon. The hatched regions indicate conditions under which the phase is predicted to be metastable— in effect, this means that multiple phases can co-exist in these regions. Using this diagram, answer the following questions concerning the phases of carbon. Note the indicated scales for the horizontal and vertical axes (1 bar = 0.0001 GPa).

**Graph Explanation:**

- **Axes:** 
  - The horizontal axis represents temperature (T) in units of \( T/1000 \, K \).
  - The vertical axis represents pressure (P) in GPa.
   
- **Phases:**
  - **Graphite Region:** Dark grey area at lower pressures and a range of temperatures.
  - **Diamond Region:** Yellow area at higher pressures.
  - **Liquid Region:** Blue area at moderate to high temperatures and pressures.
  - **Vapor Region:** Green area at high temperatures and low pressures.

- **Metastable Regions:** Hatched areas where multiple phases can exist.

**Questions:**

(a) Does graphite melt or sublime at 10 bars of pressure?

(b) If pressure remains constant, what are the possible phase transitions for diamond at 4500 K as \( T \) is increased?

(c) Identify the approximate temperature and pressure of the standard solid-liquid-gas triple point on this diagram. Are there other triple points indicated in the diagram?

(d) Estimate the maximum temperature at which graphite can exist at \( P = 1 \, GPa \). What would happen if the pressure is increased for a sample of graphite at this temperature?
Transcribed Image Text:The diagram shown below is a theoretical representation of the phase diagram for carbon. The hatched regions indicate conditions under which the phase is predicted to be metastable— in effect, this means that multiple phases can co-exist in these regions. Using this diagram, answer the following questions concerning the phases of carbon. Note the indicated scales for the horizontal and vertical axes (1 bar = 0.0001 GPa). **Graph Explanation:** - **Axes:** - The horizontal axis represents temperature (T) in units of \( T/1000 \, K \). - The vertical axis represents pressure (P) in GPa. - **Phases:** - **Graphite Region:** Dark grey area at lower pressures and a range of temperatures. - **Diamond Region:** Yellow area at higher pressures. - **Liquid Region:** Blue area at moderate to high temperatures and pressures. - **Vapor Region:** Green area at high temperatures and low pressures. - **Metastable Regions:** Hatched areas where multiple phases can exist. **Questions:** (a) Does graphite melt or sublime at 10 bars of pressure? (b) If pressure remains constant, what are the possible phase transitions for diamond at 4500 K as \( T \) is increased? (c) Identify the approximate temperature and pressure of the standard solid-liquid-gas triple point on this diagram. Are there other triple points indicated in the diagram? (d) Estimate the maximum temperature at which graphite can exist at \( P = 1 \, GPa \). What would happen if the pressure is increased for a sample of graphite at this temperature?
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