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Crystals of Epsom salt having an equivalent diameter of 1.5 cm are growing in a solution of MgSO4 at a supersaturation of 0.005 mole fraction MgSO4.7H2O and a temperature of 303 K. For saturated solution of MgSO4, the average coefficient of interfacial reaction is 0.18 gmol/cm2.h.mole fraction. The mass transfer coefficient has been estimated to be 1.75 gmol/cm2.h.mole fraction. The average density of the crystals is 1.68 g/cm3. Assuming the crystals to be cubic, calculate their growth rate in cm/h.

A gaseous mixture of SO2 and air containing 4 % SO2 by volume is to be scrubbed counter currently with water in a packed absorption column having a cross sectional area of 0.90 m2. The inlet gas rate is 30 kmol/h of a gas mixture and liquid rate is 80 kmol/h of pure water. The operating temperature and pressure are 298 K and 1 atm respectively. SO2-water solution obeys Raoult’s law and the vapour pressure of SO2 at 298 K is 99.29 kPa. Overall absorption mass transfer coefficient based on gas phase is 72 kmol/h.m3.atm. Calculate: a. The actual to minimum liquid flowrate. b. Height of the column required for 95 % absorption of SO2 from the entering gas mixture during absorption process for 1.5 times of minimum used as actual liquid flowrate.

A zero-order homogeneous gas reaction with stoichiometry A→rR proceeds in a constant volume bomb,n=1 when t=0 and n=1.5 when t=1. If the same reaction, same feed composition and initial pressure proceeds in a constant-pressure set-up, find V at t=1 if V=1 at t=0.

Water enters a heating system at a flow rate of 0.2 kg/s. The system has a thick-walled tube with inner and outer diameters of 16 and 25 mm respectively. The outer tube surface is well insulated, and there is electrical heating within the tube wall which provides a uniform generation of q = 4.7 x106 W/m3


Find the general solution of the integral equation



F(t)= aSint-2∫0^t F(u) Cos(t-u)du?

Find all possibile Taylor's series and Laurent series expansion of f(z)=1/(z+1)(z+2)² about the point z=1

Using residue theorem evaluate ∲c e^z-1/z(z-1)(z-i)² dz where C is |z|=2

Find the most general analytic finction f(z)=u+iv where the real part u(x,y)=x^2-y^2-x

Solve the Partiol differential equation (D²-D^1²)z= x² + y²

A coal contains 78% carbon, 4% hydrogen, 2% oxygen, 1.8%


sulphur and rest as non-combustibles.


Calculate:


(i) Gross calorific value of the coal in GJ/ton using Dulong’s Formula


337 C + 1442 [H – (O/8)] + 93 S kJ/kg


where C, H, O and S are percentages of carbon, Hydrogen, oxygen and


sulphur respectively.


(ii) Amount of coal needed per day to burn in a 10 MW power plant


working with 32% thermal efficiency (Given 1 kWh = 3.6 MJ).

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