1. (a)

• A small number of parameters specify the macrostate of a system, these parameters give the condition of the system at any instant of time. The values of these parameters are such that if the no. of molecules and two other variables are known, all other macroscopic parameters can be calculated and the macrostate is specified.

• Examples of variables that specify the macrostate are:

• Pressure (due to bombardment of walls by atoms/molecules of gas)
• Volume (imposed on the system by fixed boundaries or let the system find its own volume by natural expansion or contraction)
• Amount of substance (system either contains fixed no. of particles, or if particles are allowed to enter or leave the system, then the number and type of the particles that enter or leave must be known)
• Energy (kinetic energy due to atoms in motion, and potential energy due to interaction of atoms with one another – these 2 sources of energy give rise to the internal energy of the system)
• Others like external stresses, electric field strengths, magnetic field strengths, magnetisation, polarisation…Normally these parameters are assumed absent.

• The thermodynamic variables stated above can be divided into 2 types:

• State functions: Property has a value that depends on the current condition and not how the system arrived at that condition. Changes in state functions are independent of the process by which the system passes from its initial to final condition. Example of state function is work.
• Path functions: Property has a value that not only depends on the current condition of the system but also how the system arrived at that condition. Changes in state functions are dependent of the process by which the system passes from its initial to final condition. Example of path function is heat.

• State functions can be further divided into extensive and intensive properties.

• Extensive: Extensive properties depend on the volume or size of the system. Example of extensive property is internal energy.
• Intensive: Intensive property has a value at a point in the system; it is independent of the size of the system. Examples of intensive property are temperature and pressure.

(b) Refer to answers for Qn 2 (b) in Oct/Nov 1997 paper.

1. (a) Sintering refers to the bonding of fine powder particles or fibres into more dense bodies. It is usually effected only at sufficiently high temperatures. Sintering is able to take place because the total free energy of a large number of fine particles is greater than a small number of coarse particles or a solid block of equal solid volume. The driving force for sintering to take place is a reduction in the surface area and hence a reduction in the total surface energy. At high temperatures, the activation energy required for sintering to take place is overcome and the smaller mass will coalesce into a bigger mass to reduce the surface energy to reduce the total surface area.

The vapour pressure of a small particle is greater than that of a large particle – this results in the coalesce of small particles into a bigger mass at high temperatures. The relationship between the vapour pressures of 2 particles of different radius is:

RT ln p_r/p¥ = 2vs /r

The mechanism of material transport during sintering is dominated by surface and lattice diffusion. Therefore, the driving force is dependent on the diffusion coefficient. Material transport will result in necking. The rate at which the neck volume changes indicates the rate of sintering. It is determined by the rate at which atoms move in the neck area. (Draw diagram.) For a single phase material, any existing pores are filled by the vapour of the material itself.

(b) Refer to answers for Qn 1 (d) in Oct/Nov 1997 paper.

2. (a) Rhodium and Platinum, Tungsten and Tantalum.

The 2 sets of elements are completely soluble in each other in both the solid and liquid states because they have similar crystal structure (both BCC or both FCC), nearly identical atomic radii (<15%), electronegativities (do not form compounds) and valence. } Hume Rothery Solid Solution Rule

3. (a) Refer to Calister, pg 273, figure 9.24.

(b) (i) Just below the peritectic temperature, the microstructure consists of solid a and b . Just above the peritectic temperature, the microstructure consists of liquid and sollid a .

Weight fraction of a = (66.3-42.4)/(66.3-10.5) = 0.428

Weight fraction of liquid or b = (42.4-10.5)/(66.3-10.5) = 0.572

Composition of a is 10.5wt%Ag and 89.5wt%Pt.

Compostion of b or liquid is 66.3wt%Ag and 33.7wt%Pt.

(ii) Phases present are liquid and b .

Weight fraction of liquid = (60-48)/(77-48) = 0.414

Weight fraction of b = (77-60)/(77-48) = 0.586

Composition of liquid is 77wt%Ag and 23wt%Pt.

Composition of b is 48wt%Ag and 52wt%Pt.

(c) Composition of the alloy is 25.07 wt%Ag.

4. (a) 50% bainite, 50% martensite

(b) cementite and coarse pearlite

(c) 100% bainite

(d) Spheroidite

(e) cementite, fine pearlite, bainite and martensite

(f) 50% bainite, 50% martensite

(g) cementite, bainite, martensite