A student conducted an experiment and found that an ideal gas obeys the condition $\large\frac{p^2}{\rho} =$ constant. Initially the gas is at a temperature $T$, pressure $p$ and density $\rho$. The gas expands such that the density changes to $\rho/2$, which of the following is true?

Question

$(A):$ the pressure of the gas changes to $\sqrt (2p)$ $(B):$ the pressure of the gas is unchanged $(C):$ the graph of the above process on the P-T graph is a parabola $(D):$ the graph of the above process on the P-T graph is a hyperbola