FYKOS Year 28 Series 6 Problem 2 — breathe deeply · FYKOS 28 #28.6.2

Physics · mechanics · thermodynamics

Problem

Mage Greyhald celebrated his 100th birthday a long time ago and has begun to fear that Death will pay him a long delayed visit. He decided thus that he will ecase himself into a magic chest, where Death can't reach him. Unfortuntely he forgot to tell the craftsmen to add breathing holes. Air in the chest takes up a volume;V0=400lV_{0}=400l, the percentage of the volume that is oxygen is φ0=0,21φ_{0}=0,21. With every breath he uses up only k=20k=20% of the volume's oxygen Vd=0,5lV_{d}=0,5l. The frequency of breaths of the mage after the closing of the chest rises according to the relation $f(t)=f0⋅φ0φ(t) ,\\f(t)=f_0 \cdot \frac{\varphi_0}{\varphi (t)}\,, wheref_{0}=15breaths\cdot min^{−1}istheinitialbrathfrequencyis the initial brath frequency is φ(t)andthepercetageofthevolumethatisoxygenattimecase and the percetage of the volume that is oxygen at time case t.DeterminehowlonguntilDeathwillcomeforGreyhaldiftheminimumvolumeofoxygenintheairrequiredforsurvivalis. Determine how long until Death will come for Greyhald if the minimum volume of oxygen in the air required for survival is φ_{s}=0,06$.

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