In this illustration we'll discuss about mixing
of 2 substances.
we are given that when equal volume of 2 substances
are mixed together the specific gravity of
mixture is 4.
but when equal weights of the same substances
are mixed together.
the specific gravity of mixture is 3 we are
required to find the specific gravities of
the 2 substances.
here, we can consider, if, ro 1 and ro 2,
are the specific gravities. of these substances.
then.
when, mixing.
equal volumes.
v, of each.
we use, in this situation we are given that
when equal volume are mixed the specific gravity
of mixture is, 4.
so we can write, 4 would be the specific gravity
when equal volumes are mixed.
in this situation if m 1 and m 2 be the masses,
or we can say 4 is the specific gravity of
mixture.
this should be equal to.
we can write, ro 1 v. plus, ro 2 v. divided
by, 2 v. because if ro 1 ro 2 are the specific
gravities. of, individual substances then
the mass of first in terms of.
this specific gravities we can write ro 1
v and, for the other it is ro 2 v divided
by, the total volume of mixture give us the
specific gravity of mixture.
so simplifying this is giving us ro 1 plus,
ro 2 by 2. and that is say our equation 1.
and we can write when.
equal masses. of the 2 substances, are mixed.
here we use, the mixture specific gravity
is given as 3, so 3 will be equal to, m 1
plus m 2.
divided by the total volume which can be written
as, m 1 by ro 1 plus, m 2 by ro 2. and here
masses are equal so these will get cancelled
out. and we get, 2 ro 1 ro 2 upon, ro 1 plus
ro 2, that is say our equation number 2. here
we are using.
m 1 is equal to, m 2.
now in this situation if we substitute ro
1 plus ro 2 is equal to, 8 then this is give
us now from 1 and 2 we can simplify. and get
the values of ro 1 and ro 2.
so here you can see.
we'll be getting, ro 1 multiplied by ro 2
is equal to 12. and, if we, re-substitute
the value, in equation 1, this is ro 1 plus
ro 2 is 8.
so this gives us, ro 1, plus 12 by ro 1, is
equal to 8.
that is now quadratic equation. and here we
can see, the result we are getting is, ro
1 square, minus 8 ro 1.
plus 12, is equal to zero. which will result,
the value of ro 1 as, this minus b. plus minus
root of, here b square is 64, minus, 48, divided
by, 2.
so here the value of, ro 1 we are getting
is, you can see this 64 minus, 48 would be,
16, and that will be 4 so 8 plus minus 4 by
2.
so here the value of ro 1 is equal to.
either 6, or we are getting, 2.
so if these are the values of ro 1 we are
getting from this equation and we can see,
in both of these equations ro 1 and ro 2 are,
interchangeable so, if ro 1 is 6 here ro 2
will be equal to, 2. this implies.
here, if we consider ro 1 is equal to 6 then
ro 2 will be equal to 2 so these are the specific
gravity. of the substances and that will be
the result of this problem.
