Question

What is the relationship between density and pressure?

• A. $\frac{d_1}{p_1}=\frac{d_2}{p_2}$
• B. $\frac{d_1}{p_2}=\frac{d_2}{p_1}$
• C. $d_1=2p_1$
• D. $d_2=2p_2$

Answer 1

The correct option is A

$\frac{d_1}{p_1}=\frac{d_2}{p_2}$

We know that according to Boyle's Law,

$V\propto \frac{1}{P}$ (Temp. constant)

But also know that, $d=\frac{m}{v}$

$P_1{V}_1=P_2{V}_2$

$V=\frac{m}{d}\Rightarrow V\propto \frac{1}{d}$

And $V\propto \frac{1}{P}$

$\Rightarrow \frac{1}{d}\propto \frac{1}{p}\Rightarrow d\propto p$ (where T is constant)

$\Rightarrow \frac{d_1}{p_1}=\frac{d_2}{p_2}$