Consider the pneumatic system shown on the bottom, in which a tank of volume $V$ is filled with gas through a valve with

resistance $R.$ The density of the gas at the entrance to the tank is ${}_{in},$ it's pressure $($before passing through the valve$)$ is

$p_{in}$ and the volume flow of the gas into the tank is $q_{in}.$ Assuming ideal gas and constant temperature, it is known that

${}^{}=\frac{1}{R_{S}T}{p}^{},$ where $R_S$ is the specific gas constant, $T$ is the temperature of the gas, $$ is the gas's density, and $p$ is its

pressure.

Which of the following statements is true for the linear system whose input is $p_{in}(t)$ and output is the gas pressure inside

the tank, $p(t)?$

A$.$ The DC gain of the system is $\frac{1}{R}.$

B$.$ The system is unstable.

C$.$ The time constant of the system is $\frac{VR}{R_{s}T}.$

D$.$ The time constant of the system is $\frac{R_{s}T}{VR}.$

Help me solve this, thanks