Question

If $P$ is pressure and $\rho$ is density of a gas, then $P$ and $\rho$ are related as

• A. $P \propto \rho$
• B. $P \propto (1/ ?)$
• C. $P \propto p^2$
• D. $P \propto (1/ \rho^2)$

Answer 1

Answer: (A)

$P \propto \rho$

Answer 2

Ideal gas equation is given as: $PV = nRT$ $P =$ Pressure of gas, $V =$ volume of gas $n =$ moles of gas, $R =$ gas constant $T=$ temperature $\Rightarrow P V=\frac{w}{M} R T$ $w =$ mass of gas $M =$ Molecular mass of gas $P=\left(\frac{w}{V}\right) \frac{R T}{M}$ $\Rightarrow P=\rho \frac{R T}{M}$ $\left(A s \rho=\frac{w}{V}\right)$ $\Rightarrow P \mu \rho$