$1.$ Consider a large tank with a fixed volume $(\backslash (\backslash$left$.\backslash$mathrm$\{$V$\}=\backslash$mathrm$\{$V$\}0\backslash$left$[\backslash$mathrm$\{$~m$\}^\{3\}\backslash$right$]\backslash$right$)\backslash ).$

The initial internal pressure of the tank is $\backslash (\backslash$mathrm$\{$P$\}=\backslash$mathrm$\{$P$\}0[\backslash$mathrm$\{$~Pa$\}]\backslash ).$

There are two tubes attached each delivering oxygen to the tank.

The volumetric flow rate of oxygen for each tube is Qin $=$ Q$1[\backslash (\backslash$left$.\backslash$mathrm$\{$m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash$right$]\backslash )).$

$1\mathrm{.}1.$ Draw a diagram for the system and clearly label each of the given parameters. $(4$ points$)$

$1\mathrm{.}2.$ Develop an expression for time that it would take for the pressure of the tank to reach $($Pf $=\backslash (10\backslash$mathrm$\{$PO$\}[\backslash$mathrm$\{$Pa$\}]\backslash )).$

Hint $1$: $\backslash (\backslash$rho$=\backslash$frac$\{$M P$\}\{$R T$\}\backslash )($here M is the molar mass of the gas, R is gas law constant, T is temperature$)$

$1\mathrm{.}3.$ Consider that the Volume of the tank is no longer fixed and is changing as a function of time. Using math show, how would your answer from the previous part $(1\mathrm{.}2.)$ changes.

You do not have to solve the resulting expressions.