[senthil]

1. A solid is soluble in a solvent up to a maximum (i.e. saturation) concentration of 0.33 g/mL. The rate
at which it dissolves in the solvent varies directly as the product of the amount of undissolved solid
present in the solvent and the difference between the saturation concentration and the instantaneous
concentration. In an experiment, 20 g of the solid is added to 120 mL of solvent. When the
concentration is measured after 12 minutes, it is found to be 0.033 g/mL. Find the dissolved amount
of solid at any time ‘t’.

2. A first order reaction in which a chemical species being converted to another is described by the
differential equation: kC
dt
dC = − , where C is the concentration of the species at time ‘t’ and ‘k’ is
the rate constant. A certain material ‘A’ is placed in a reaction vessel. ‘A’ is converted to ‘B’; ‘B’,
in turn, undergoes reaction to form ‘D’. If CA0 is the initial concentration of ‘A’ in the reactor, find
an expression for concentration of ‘B’ as a function of time. Take kA and kB to be the rate constants
for conversion of A and B, respectively. The rate of formation of ‘B’ is also the rate of conversion
of ‘A’.

3. Heat conduction in a solid cylinder is described by the differential equation
K d T^2/ dx^2 = − 2

where T is temperature at position ‘x’ along the length of the cylinder, K is thermal conductivity (a constant)
and Q is the heat generated in the solid per unit volume per unit time. A rod of length L and diameter
d is used as a heating element. The heat generated per unit time per unit volume varies linearly along
the length of the rod, i.e., (Q = a.x). The temperatures at the ends of the rod are T1 and T2,
respectively. Where does the maximum temperature occur in the rod? For what value of the
constant ‘a’ will the maximum temperature occur at the mid-point along the length of the rod?
Neglect heat conduction in the radial direction.

[eugenedakin]

Hello senthil,

As part of the policy of this forum, we are only allowed to help you with your questions, and not complete them for you.  Please work through the problem as much as you can, place the results on the forum for others to help.

Thanks for your time and consideration.

Sincerely,

Eugene