Holooly Plus Logo
Holooly Plus Logo

Question 6.13: A phase diagram is drawn for a mixture of two substances at ...

A phase diagram is drawn for a mixture of two substances at a fixed pressure p with one liquid phase and two solid phases (Fig 6.6). The substances are labelled 1 and 2 and the diagram is shown as a function of the concentration c_1 of substance 1. This diagram presents what is called a eutectic point. At the eutectic concentration c^E_1 , the freezing temperature is the lowest. In particular, it is lower than the freezing temperatures of the pure substances (points C and D). At the eutectic, the liquid freezes into a mixture of two solid phases, the α and β phases.
a) Consider a liquid at concentration c^A_1 . As the temperature is lowered, the point A is reached. Describe qualitatively what happens then.
b) Describe what happens if a liquid of composition c^E_1 is cooled.

The Blue Check Mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.

a) At point A, the solid phase α starts to precipitate. Notice that the concentration c^B_1 of solid thus formed is different from the concentration c^A_1 of liquid.
b) At point E, the entire solution becomes a solid alloy. The concentrations of the solid phases α and β in the alloy are given by the lever rule with respect to point E.

Related Answered Questions

A phase diagram is drawn for a mixture of two substances at a fixed pressure p with a liquid phase and a gaseous phase (Fig. 6.5). The substances are labelled 1 and 2 and the diagram is shown as a function of the concentration c1 of substance 1. There is a range of temperature for which there is

Verified Answer:
a) According to Gibbs phase rule (6.62) r = 2 and ...

Consider a cloud of droplets and assume that they all have the same diameter r. According to the Laplace formula (exercise 4.8), the pressure p (r) inside the droplets of radius r is related to the vapour pressure p0 (r) by, p (r) = p0 (r) + 2 γ/r where γ is the surface tension. We note p∞ the

Verified Answer:
The equilibrium between the liquid and the gas is ...

To establish the positivity of the specific heat at constant pressure Cp compressibility coefficient at constant temperature κT (see relations (6.31)), follow the steps given below: a) Show that the Mayer relation (5.42) can be recast as, Cp = CV + α²/κT VT where α is the thermal coefficient of

Verified Answer:
a) The Mayer relation yields, C_p = C_V + ...

A liquid is at equilibrium with its vapour. The vapour is assumed to be an ideal gas. The liquid has a molar latent heat of vaporisation llg that depends on temperature, with llg = A− BT, where A and B are constants. Apply the Clausius–Clapeyron relation (6.50) and consider that the molar volume

Verified Answer:
Neglecting the molar volume of the liquid phase co...

A steel wire is wrapped over a block of ice with two heavy weights attached to the ends of the wire. The wire passes through a block of ice without cutting the block in two. The ice melts under the wire and the water freezes again above the wire. The wire is considered a rigid rod of negligible

Verified Answer:
The process of ice melting due to the pressure exe...

Water is cooled with ice cubes (Fig. 6.10). The water and the ice cubes are considered as an isolated system. Initially, the ice cubes are at melting temperature T0 and the water at temperature Ti. The total initial mass of ice is M’ and the initial mass of water is M. The latent heat of melting

Verified Answer:
Heat is transferred from the water to melt the ice...

A mixture of ice and water is heated up in such a way that the ice melts. The ice melts at a rate r and the molar latent heat of ice melting is lsl. a) Determine the thermal power PQ transferred to the ice. b) Determine the entropy rate of change S˙.Numerical Application:Ω= 2.0·10^−2 mol s^−1

Verified Answer:
a) The thermal power transferred to the ice is, [l...

A van der Waals gas is going through a Joule-Thomson process that keeps the enthalpy H constant (problem 4.8.3). A van der Waals gas in characterised by the following equations of state,p = NR T/ V − Nb – N² a/V² and U = cNRT − N² α/V and the amount of gas is constant, i.e. N = const. Use the

Verified Answer:
The enthalpy for a van der Waals gas reads, [latex...

A mole of oxygen, considered as a van der Waals gas, undergoes a reversible isothermal expansion at fixed temperature T0 from an initial volume Vi to a final volume Vf. Determine the work Wif performed on the van der Waals gas in terms of the parameters a, and b. Numerical Application: T0 = 273 K

Verified Answer:
For one mole of oxygen at temperature T_0[/...

The surface tension modifies the melting point of particles. The effect is important effect when the diameter is in the nanometer range. A differential equation has to be written for Tm (r), the melting temperature of particles of radius r. In order to perform this thermodynamical analysis, assume

Verified Answer:
The chemical equilibrium between an infinitely lar...