Consider a simple one component system at a constant pressure P. The chemical potential for the solid (s), liquid (1), and gas (g) phases vary with temperature according to the following expressions: kJ µ„(T)= -600–107k-.o1(/k) m kJ 4, (T)= +500– 20K-.02(/K) %3D kJ 4,(T)= +7700– 50K-.05(7k)

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Identify the phase transitions that occur for this system as the temperature varies at constant pressure. Determine the coexistence temperatures and the temperature range over which each phase is stable. 

Consider a simple one component system at a constant pressure \( P \). The chemical potential for the solid (s), liquid (l), and gas (g) phases vary with temperature according to the following expressions:

\[
\mu_s(T) = \left[ -600 - 10 \frac{T}{K} - 0.01 \left( \frac{T}{K} \right)^2 \right] \frac{\text{kJ}}{\text{mol}}
\]

\[
\mu_l(T) = \left[ +500 - 20 \frac{T}{K} - 0.02 \left( \frac{T}{K} \right)^2 \right] \frac{\text{kJ}}{\text{mol}}
\]

\[
\mu_g(T) = \left[ +7700 - 50 \frac{T}{K} - 0.05 \left( \frac{T}{K} \right)^2 \right] \frac{\text{kJ}}{\text{mol}}
\]

These expressions describe how the chemical potential (\(\mu\)) of each phase (solid, liquid, gas) changes with temperature (\(T\)) at a constant pressure \(P\). The coefficients in each equation can be interpreted as follows: a constant term, a temperature-dependent linear term, and a temperature-dependent quadratic term. Each unit is given in kilojoules per mole (\(\text{kJ/mol}\)).
Transcribed Image Text:Consider a simple one component system at a constant pressure \( P \). The chemical potential for the solid (s), liquid (l), and gas (g) phases vary with temperature according to the following expressions: \[ \mu_s(T) = \left[ -600 - 10 \frac{T}{K} - 0.01 \left( \frac{T}{K} \right)^2 \right] \frac{\text{kJ}}{\text{mol}} \] \[ \mu_l(T) = \left[ +500 - 20 \frac{T}{K} - 0.02 \left( \frac{T}{K} \right)^2 \right] \frac{\text{kJ}}{\text{mol}} \] \[ \mu_g(T) = \left[ +7700 - 50 \frac{T}{K} - 0.05 \left( \frac{T}{K} \right)^2 \right] \frac{\text{kJ}}{\text{mol}} \] These expressions describe how the chemical potential (\(\mu\)) of each phase (solid, liquid, gas) changes with temperature (\(T\)) at a constant pressure \(P\). The coefficients in each equation can be interpreted as follows: a constant term, a temperature-dependent linear term, and a temperature-dependent quadratic term. Each unit is given in kilojoules per mole (\(\text{kJ/mol}\)).
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