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 `sqrt2 P`
B. The temperature of the gas changes to `sqrt2 r`
C. The graph of the above process on P-T diagram is parabola
D. The graph of the above process on P-T diagram is hyperbola

Answer

B, D

Explanation

`P^2 // rho = "constatnt "rArr P^2 V = "constant " "rArr" P(T) = constant "rArr " "p prop 1/T`
Now `P^2/rho = P_2^2/(rho //2) rArr P_2 = P/sqrt2 rArr T_2 = sqrt2 T`