# Important Thermodynamic equations

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Important Thermodynamic equations

Conditions for equilibrium between Phases

Various Equilibrium conditions
Capacity Factor Intensity Equilibrium Condition S T At const. U,V V P At const. V,T ni i At const. P,T

Chemical Potential

Intergration of function

Phase changes of pure component

Physical meaning of Chemical potential
Tendency of a system to give particles.

Temperature dependence of phase stability

Ice-skating As we glide across the ice, we exert pressure on the thin blade, and are therefore creating a small stream of water in our path by melting that ice. The water between the blade and the ice is what we really glide across.

Response of melting temperature to the applied pressure

Relationship between equilibrium temperature and pressure

e.g. Solid-liquid equilibria

Relation between dp and dT

The solid –liquid boundary

Liquid –Vapour boundary

Solid-Vapour Boundary
1 bar

Elevation of boiling point
Boiling point of water is raised if the pressure above water is increased; it is lowered if the pressure is reduced. This explains why water boils at 70 °C up in the Himalaya

Elevation of boiling point
An application of this effect is the pressure cooker. A pressure cooker traps steam inside it, raising the pressure to about twice the atmospheric pressure. As a result, the water boils at 120 °C. Food cooks quicker at the higher temperature. There is a safety valve on the cover which opens if the pressure is too high.

Autoclave Sterilization of both materials and contaminated media is an essential process in a laboratory for in vitro cultures. This sterilization is usually done in a device called an autoclave. Essentially, an autoclave is a container that exposes the material to be sterilized to temperatures above the boiling point of water, which is achieved by increasing pressure.

Q. It has been suggested that the surface melting of ice plays a role in enabling speed skaters to achieve peak performance. Carry out the following calculation to test this hypothesis. At 1 atm pressure, ice melts at K, ΔHf =6010 J mol-1, the density of ice is 920 Kg m-3, and the density of liquid water is 997 kg m-3. What pressure is required to lower the melting temperature by 5.0 ºC ? (b) Assume the width of the skate in contact with ice has been reduced by sharpening to 25*10-3 cm, and that the length of the contact area is 15 cm. If the skater of mass 85 kg is balanced on one skate, what pressure is exerted at the interface of the skate and the ice ? ©What is the melting point of ice under this pressure? (d) If the temperature of ice is -5 ºC, do you expect melting of ice at ice-skate interface to occur ?

DH of vaporization of water is cal/g at the normal boiling point. Many bacteria can survive at 100 C by forming spores. Hence autoclaves used to sterlize medical and laboratory instruments are pressurized to raise the boiling point of water to 120 C. What will be the pressure required to increase the boiling point of water to 120 ºC ?

Q. Ar has normal melting and boiling points of 83. 8 and 87
Q. Ar has normal melting and boiling points of 83.8 and 87.3 K; its triple point is at 83.8 K and 0.7 atm, and its critical temperature and pressure are 151 K and 48 atm. State whether Ar is a solid, liquid, or gas under each of the following conditions (a) 0.9 atm and 90 K (b) 0.7 atm and 80 K (c) 0.8 atm and 88 K (d) 0.8 atm and 84 K (e) 1.2 atm and 83.5 K.

Q. Dry ice is frozen carbondioxide
Q. Dry ice is frozen carbondioxide. A block of dry ice has a surface temperature of C. If you want to send something frozen across the country, you can pack it in dry ice. It will be frozen when it reaches its destination, and there will be no messy liquid left over like you would have with normal ice. Explain this phenomenon with the help of a phase diagram?

The vapor pressure of zinc varies with temperature as
log p (mmHg)= -6850/T – 0.755log T and that of liquid Zn as log p (mmHg) = -6620/T log T calculate (a) boiling pt of Zn. (b) the triple point. © the heat of evaporation at the boiling point. (d) heat of fusion. (e) the difference in Cps of solid and liquid Zn.

The effect of applied pressure on vapor pressure

Phase Rule F=C-P+2 C = number of component

Degree of Freedom Number of independent intensive variables needed to specify its intensive state. T, P and mole fraction in each phase.

Total number of intensive variable = pc +2
Mole fraction of components in each phase must be one Number of relation =number of phases= p For chemical equilibrium, Chemical potential of individual component will be same in each of the phases. In each of the component (p-1) relation for each of the component Total number of relation for chemical equilibrium = c(p-1) Degree of Freedom = pc + 2 – p - c(p-1) = c – p + 2

What happens to boiling point or freezing point of a liquid in the presence of a solute?
What happens to chemical potential of a liquid in the presence of solute?

There is elevation of boiling point upon addition of a solute.
There is depression of freezing point upon addition of a solute.