A flask contains 100 c.c of a liquid at `10^(@)C`. When it is heated to `110^(@)C` increase in volume of the liquid appears to be 2 c.c. Find the coefficient of real expansion of the liquid.
(`alpha` of flask is `11xx10^(-6)//""^(@)C`).

Explanation

Initial volume of the liquid `(v _(1)) = 100 c.c`
Initial temperature `(t _(1)) = 10 ^(@)C,` Final temperature `(t _(2)) = 110 ^(@) C`
Apparent increase in volume `= (v _(2) -v _(1)) = 2c.c,` Coefficient of apparent expancion
`gamma _(a) = (v _(2) -v _(t))/( v _(1) (t _(2) - t _(1))) = (2)/( 100 (11- 10 )) = 2 xx 10 ^(-4) //^(@)C`
Coefficient of cubical expansion of the flask `(220-620)/(0.20-92200 -29)= (130)/(2005) = 3 xx 11 xx 10 ^(-6) = 33 xx 10 ^(-5) // ^(@)C`
Coefficient of real expansion of the liquid, `gamma _(R ) =gamma _(a) + gamma = 2 xx 10 ^(-4) + 33 xx 10 ^(-6) = 2 xx 10 ^(-4) + 0.33 + 10 ^(-4)`
`therefore gamma _(R ) = 2.33 xx 10 ^(-4) //^(@)C`