If two miscible liquids of same volume but different densities P1 and P2 are mixed, then the density of the mixture is given by
(P<sub>1</sub> + P<sub>2</sub>) / 2
2P<sub>1</sub>P<sub>2</sub> / (P<sub>1</sub> + P<sub>2</sub>)
2P<sub>1</sub>P<sub>2</sub> / (P<sub>1</sub> - P<sub>2</sub>)
P<sub>1</sub>P<sub>2</sub> / (P<sub>1</sub> + P<sub>2</sub>)
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CDS-2 – 2018
The mass of the first liquid is m₁ = density × volume = P₁V.
The mass of the second liquid is m₂ = density × volume = P₂V.
The total mass of the mixture is m_total = m₁ + m₂ = P₁V + P₂V = (P₁ + P₂)V.
The density of the mixture is ρ_mixture = m_total / V_total = (P₁ + P₂)V / (2V) = (P₁ + P₂) / 2.
This formula is valid when equal volumes of two miscible liquids are mixed.
– When mixing, total mass is the sum of individual masses, and total volume is the sum of individual volumes (assuming no volume change upon mixing, which is typical for miscible liquids unless otherwise specified).
– The calculation is based on the given condition that the liquids have the ‘same volume’.