A given mass of a gas is subjected to an external pressure of `0.5 xx 10^(10) Nm^(-2)` the bulk modulus of the gas is `0.5 xx10^(10) Nm^(-2)` Find the ratio of the density of the gas before and after applying the external pressure.

Answer

` 1 : 2`

Explanation

Density, `rho = M//V` Taking log on both the sides and differentiating, we get, `(Delta rho)/(rho) = -(Delta V)/(V)`
`Now, B = (Delta rho)/((Delta V//V)) = (0.5xx10^(10))/((Delta rho//rho))`
`or (Delta rho)/(rho) = (0.5xx10^(10))/(B)j = (0.5xx10^(10))/(0.5 xx10^(10)) = 1`
`or Delta rho = rho`
Therefore, `rho' = rho + Delta rho = rho + rho = 2rho`
`Hence, (rho)/(rho') = (rho)/(2rho) = (1)/(2)`