# Consider two fluids having specific volumes as S1 and S2. What would be the relation between their mass densities (d1 and d2 respectively) if S1 < S2?

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Consider two fluids having specific volumes as S1 and S2. What would be the relation between their mass densities (d1 and d2 respectively) if S1 < S2?.
1. d1 > d2
2. d1 = d2
3. d1 < d2
4. cannot be determined

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Correct Answer - Option 1 : d1 > d2

Concept:

Let consider the volume of two fluids is V1 and V2 and the masses of fluid m1 and m2 respectively.

Now

Specific Volume - It is a property of materials, defined as the number of cubic meters occupied by one kilogram of a particular substance.

So, Specific volumes for two fluids are as follows

S1 = V1 / m1      . ...........(i)

S2 = V2 / m2      .............(ii)

Using the relationship between mass density, the mass of fluid, and volumes

$Mass\space density = {Mass \over Volume}$

Assume the mass density of the above fluids is d1 and d2, hence

$d_1 ={m_1 \over V_1}\space and \space d_2 ={m_2 \over V_2}$

Then the relation between specific volume and mass density of fluids by using equations (i) and (ii)

S1 = 1 / d1 and S2 = 1 / d2

So the relation between specific volume and mass density is inversely proportional to each other.

Hence, in this question given that the specific volume of two fluids is S1 < S2 , so mass density is d1 > d2.