Question

At $0^{\circ }C$, the value of the density of a fixed mass of an ideal gas divided by its pressure is $x$. At ${100}^{\circ }C$, this quotient is

• A. $\frac{100}{273}x$
• B. $\frac{273}{100}x$
• C. $\frac{273}{373}x$
• D. $\frac{373}{273}x$

Answer 1

The correct option is C $\frac{273}{373}x$

Using $P=\frac{\rho RT}{M_w}$
$\frac{\rho }{P}=\frac{M_w}{RT}\Rightarrow {\left(\frac{\rho }{P}\right)}_{0^{\circ }C}=\frac{M_w}{R\times 273}=x...\left(1\right)$
$\Rightarrow {\left(\frac{\rho }{P}\right)}_{{100}^{\circ }C}=\frac{M_w}{R\times 373}=y...\left(2\right)$
dividing equation. ..(1) and ..(2)
$y=\frac{273}{373}x$