Question

Sow that if Δρ , the change in density , is very small compared to the original density ρ , then the relation p = - K ( Δ v / v ) can be replaced by the relation p = K ( Δ p / p ) [ K = bulk modulus ] .

# Proper explanation
# Correct and detailed steps

Answer 1

$p \: = \frac{ - k}{ \binom{ \∆ v}{v} }$

$p = \binom{k}{v}$

p v = Constant

Differentiate between both sides

$pdv + vdp = 0$

$pdv = - vde$

$\frac{dv}{v} = \frac{dp}{p}$

∆v / v = ∆p / p ----------> 2

p = k / (∆ p)/ p

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