During an experiment, an ideal gas is found to obey a condition `(p^2)/(rho) = "constant"`. (`rho` = density of the gas). The gas is initially at temperature (T), pressure (p) and density `rho`. The gas expands such that density changes to `rho//2`.

Options

A. The pressure of the gas changes to `sqrt(2)P`.
B. The temperature of the gas changes to `sqrt(2)T`.
C. The graph of the above process on the `P-T` diagram is parabola.
D. The graph of the above process on the `P-T` diagram is hyperbola.

Answer

B, D

Explanation

Equation of process `rArr (P^(2))/(rho) =` constant `=C …..(1)`
Equation of state `(P)/(rho) = (nR)/(M)T …….(2)`
From 1 and 2
`PT =` constant `rArr C` is false, `D` is true.
As `rho`-changes to `(rho)/(2) rArr P` changes to `(P)/(sqrt(2))`
from equation `(1) rArr A` is false.
Hence `T` changes to `sqrt(21) rArr B` is true.