If the compressibility of water is σ per unit atmospheric pressure, then the decrease in volume ( V ) due to atmospheric pressure p will be

Question

If the compressibility of water is σ per unit atmospheric pressure, then the decrease in volume ( V ) due to atmospheric pressure p will be (A) σ p / V (B) σ p V (C) σ / p V (D) σ V / p

Tardigrade Admin · Accepted Answer

As, K=(p/(Δ V)V) (Here, K= bulk modulus of elasticity) or (1/K)=(Δ V / V/p) or σ=(Δ V/p V) or Δ V=σ p V

Q. If the compressibility of water is $σ$ per unit atmospheric pressure, then the decrease in volume ( $V$ ) due to atmospheric pressure $p$ will be

$σ p / V$

$σ p V$

$σ / p V$

$σV / p$

As, $K = \frac{p}{\frac{Δ V}{V}}$ (Here, $K =$ bulk modulus of elasticity)
or $\frac{1}{K} = \frac{Δ V / V}{p}$
or $σ = \frac{Δ V}{p V}$
or $Δ V = σ p V$

Q. If the compressibility of water is σ per unit atmospheric pressure, then the decrease in volume ( V ) due to atmospheric pressure p will be

σp/V

σpV

σ/pV

σV/p