Thermodynamics: Entropy and its measurement

Entropy is a property of the system used to find the direction of a process.  It is calculated as [dQ(rev)/T] for a change of state. If we have a reversible process the change in total entropy (system + surrounding) is zero and if the process is irreversible, the change in total entropy is positive. Entropy is a state function, then why does it care about the process whether it is reversible or irreversible?

Change in entropy of system will remain same whether the process is reversible or irreversible. It depends only on the states of the system. But the states of surrounding will depend on the path taken to carry out changes in the state of a system. Therefore the states of surrounding will be different for different paths taken to carry out changes in system. Hence the entropy of surrounding will change with the path. That's why the total entropy change will depend on the path taken. For a reversible process minimum amount of heat is required to get a specified amount of work. Therefore the entropy change will be minimum i.e. zero. and if the process is irreversible the amount of heat will increase resulting in positive entropy change. So it is said that Entropy of the universe never decreases.

Save energy for better tomorrow

Energy is a major concern today. The petroleum resources are depleting and the renewable sources except hydro power have their limitations. The major source of energy will be nuclear in the future, but one way we all can produce energy i.e. by saving it today.  

To save energy, we switch off the equipments like fan, bulb, TV etc, but how can we say that energy has been saved? If we take an example of AC diesel generator, if we are not taking any power from it, are we saving energy in terms of fuels? The generator will consume fuel, similar will be case with thermal plant. They are producing electricity, we use it or not, it will consume fuel. Then how do we save it?

As we switch off the lights, fans, or other equipment on a large scale, the load on plant reduces, which will make it consume less fuel. One fan or bulb may not contribute a lot, but it will be added for every equipment which is put off and collectively it will make a difference. The plant will consume fuel according to the base load, whether we use it or not, but as the load increases, the fuel consumption will increase. So save electricity save fuel save future. 

Mechanical Operation: Screen Efficiency/Effectiveness

Screens are used to separate particles based on their sizes. Separation is important for various processes in chemical industries. The efficiency of a screen is defined as the sharp separation of particles. An ideal screen means all desired particles (specified particle size) are recovered 100% from the feed and no undesired particles come with the desired one. 

the efficiency of screen depends on

1. When the screens are used for many times, the screen gets damaged. The wires displace from their original position which leads to changes in mesh opening.

2. The time of operation and capacity (i.e. feed rate) also affect the effectiveness of screen. 

3. Moisture content also effect the effectiveness of screen.

4. orientation of particle

The efficiency of screen is defined as : recovery × rejection

Recovery: the fraction of desired particle recovered from feed:P(yP)/F(yF) 

Rejection: the fraction of undesired particle rejected:R(1-yR)/F(1-yF)

F, P, R are the feed rate, product (desired size) and reject flow rate.

yF, yP, yR are the fraction of desired product in feed, product and reject.

ideally yP should be 1 and yR should be 0 and the recovery and rejection both should be 1

Now the question rises how to find yF, yP, yR?

suppose we have a mixture of 3 different sizes material say 4, 5 and 6 cm & 5 cm is the desired size particle, now, how can we calculate the mass fraction of 5 cm size particle?

In industrial screens there will be some overlapping of particle sizes, i.e. there will be presence of oversize material and undersized  particle in streams. for that we will use new screens on a sample of 3 streams which has an efficiency of 1 (new screen, less capacity, standard moisture content and proper orientation). this fraction calculated will be used to find the efficiency of the industrial screen.  

Thermodynamics: Solution Property based Problems

1. A binary mixture containing species 1 and 2 forms an azeotrope at 105.4°C and 1.013 bar. The liquid phase mole fraction of component 1 of this azeotrope is 0.62. At this temperature, the pure component vapour pressure for species 1 and 2 are 0.878 bar and 0.665 bar respectively. Assume that the vapour phase is an ideal gas mixture. Find the activity coefficients in a solution containing 40% of species1.      

2.      At 25°C and atmospheric pressure the volume change of mixing of binary liquid mixtures of species 1 and 2 is given by the equation:

∆V=  x1x2(45x1 +25x2 )

Where ∆V is in cm³/mol, at these conditions V₁=110 and V₂= 90 cm³/mol. Determine the partial molar volumes  in a mixture containing 40 mol% of species 1 at given conditions.                       

3. The partial pressure (approximate) of alcohol in alcohol water system behaviour can be represented in the figure below. The figure is divided in three sections. Select the suitable equation from Raoutlt's Law, Modified Raoult's Law and Henry Law for partial pressure applicable in these regions.

4. Fugacity coefficient of species (i ) in solution and activity coefficient of species (i) in solution

Mechanical Operation: Sphericity

Sphericity is a shape factor used to find the resemblance shape of irregular particles with a spherical particles. A spherical particle is symmetrical and has no orientation issue. there are correlations which can be used for a spherical particles like pressure drop in fluidised bed. In order to use the correlation for irregular shape particle, sphericity is used. 

Sphericity is defined as surface-volume ratio for a sphere of diameter Dp divided by the surface-volume ratio for the particle whose nominal size is Dp. The nominal diameter of the particle is generally found from screen analysis and the diameter of sphere is calculated by equating the volume of particle equal to sphere. The maximum value of sphericity is 1, because a sphere has minimum surface area for a given volume among all shape.  

Thermodynamics: Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic property of great importance defined by the expression:
G = H - TS. Enthalpy (H) is the maximum energy that a system can have at a particular state and the energy (TS) is the energy that has to be rejected to surrounding according to the 2nd law of thermodynamics. Therefore G represents the maximum usable energy that we can extract from the system at constant temperature and pressure.

For an open system the differential form of Gibbs free energy having its variables pressure and temperature are easily measured and controllable. Most chemical reactions occur at constant temperature and pressure. The partial molar Gibbs free energy has a special name i.e. chemical potential.

The other properties can also be expressed in terms of Gibbs free energy. Therefore, it is also termed as generating function.

Thermodynamics: Maxwell Equations Significance and understanding

Enthalpy and Internal energy for an ideal gas is a function of temperature only, but for real gases these also depends on one other parameter i.e. volume or pressure. In order to find change in internal energy and enthalpy for a real gas we need to get the expression in terms of measuring parameters like pressure, temperature and volume. Entropy is one important parameter in determining the change in internal energy and enthalpy for real gases. So it is necessary to first find change in entropy with pressure, temperature and volume keeping one other parameter constant. Maxwell equations tell the change in entropy w.r.t. pressure and volume.


 

These equations look somewhat difficult but there is an easier way to understand these equations:

every relation hold the change in entropy with volume at constant T & P and change in entropy with pressure at constant T & V. 

if we see the dimensional consistency, the terms W=-PdV and Q_Rev = TdS have the units of energy. So, these appear in opposite positions in the equations on left and right sides to make the equations dimensionally consistent. so like dS/dV=dP/dT

Now we have to see the constraint, like temperature. Temperature is in denominator on the right, so if we want it on left, then the constraint on the right will be V, (i.e. denominator on the left). 

Now the sign convention, when the volume increases of the system, the entropy increases, so the change in entropy with volume is positive, and when the pressure increases, the entropy decreases so the change in entropy with pressure is negative, and there will be a negative sign with the equations of change in entropy with pressure.