At `10^(@)C`, the value of the density of a fixed mass of an ideal gas divided by its pressure is x. at `110^(@)C`, this ratio is

Options

A. `x`
B. `(383)/(283)x`
C. `(10)/(110)x`
D. `(283)/(383)x`

Answer

D

Explanation

We know that `sqrt((P)/(rho))propsqrt(T)`
`:. (rho)/(P)prop(1)/(T)`
`((rho//P)_(110^(@)C))/((rho//P)_(10^(@)C))=((T)_(10^(@)C))/((T)_(110^(@)C))=(273+10)/(273+110)=(283)/(383)`
`(rho//P)_(110^(@)C)=(283)/(383)(rho//P)_(10)=(283)/(383)x`