Question

A liquid has a specific gravity of 1.1 at room temperature. What is its (a) Density at room temperature in kg/m3 (b) Specific volume at room temperature in ft3/lbm? (c) If the liquid is placed in a 2 L bottle that has a mass of 157 g, how much will the full bottle weigh?

Answer 1

To solve this problem we will proceed to find the density from the specific gravity. Later we will find the specific volume as the inverse of the density. Finally with the data obtained we will find the total weight in the bottle.

a) $\rho = \gamma * 1000$

Here,

$\rho$ = Density

$\gamma$ = Specific gravity

$\rho = 1.1 * 1000$

$\rho = 1100 kg/m3$

b)

$\text{Specific volume}= \frac{1}{\rho}$

$\upsilon = \frac{1}{1100}$

$\upsilon = 0.00090909 m^3/kg$

From the equivalences of meters to feet and kilograms to pounds, we have to

$1m = 3.280839895 ft$

$1 kg = 2.2046 lbm$

Converting the previous value to British units:

$\upsilon = 0.00090909 m^3/kg (\frac{3.280839895^3 ft^3}{1m^3} )(\frac{1kg}{2.2046 lbm})$

$\upsilon= 0.0145757 ft^3 / lbm$

c)

$V = 2*10^{-3} m^3$

Mass of the liquid in bottle is

$m = V\rho$

$m= (2*10^{-3} m^3 )(1100kg/m^3)$

$m = 2.2kg = 2200g$

Therefore the Total weight

$W= 157 + 2200 = 2357 g$