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 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 `P-T` diagram is parabola
D. the graph of the above process on the `P-T` diagram is hyperbola

Answer

B, D

Explanation

`(P_(1)^(2))/(rho_(1))=(P_(2)^(2))/(rho_(2))implies(P_(2)^(2))/((rho)/(I))=(P_(1)^(2))/(rho)`
`impliesP_(2)=(P)/(sqrt(2))`
`P=(rhoRT)/(M)`
`(P^(2))/(rho)=(rho^(2)R^(2)T^(2))/(mrho)impliesrhot^(2)=` constant
`rhoT^(2)=(rho)/(2)T_(2)^(2)`
`T_(2)=sqrt(2)T`