Answer
$67.03\space m^{3}$
Work Step by Step
Here we use the ideal gas law $PV=nRT$ to find the oxygen volume administrated to the patient.
*For the patient :-
$P_{1}V_{1}=nRT_{1}=>\frac{P_{1}V_{1}}{T_{1}}=nR-(1)$
*For the tank :-
$P_{2}V_{2}=nRT_{2}=>\frac{P_{2}V_{2}}{T_{2}}=nR-(2)$
(1)=(2)=>
$\frac{P_{1}V_{1}}{T_{1}}=\frac{P_{2}V_{2}}{T_{2}}=>V_{1}=\frac{P_{2}V_{2}T_{1}}{P_{1}T_{2}}$
Let's plug known values into this equation.
$V_{1}=\frac{(297\space K)(65\space atm)(1\space m^{3})}{(1\space atm)(288\space K)}=67.03\space m^{3}$
