Legend has it that, many centuries ago, archimedes jumped out of his bathtub and ran across town nakedscreaming "eureka! " after he solved an especially difficultproblem. though you may not have thought of things this way before, when you drink a glass of water, the water that you are drinkingcontains some water molecules that were in archimedes' bathwaterthat day, because water doesn't get created or destroyed on a largescale. it follows the water cycle, which includes rain, evaporation, flowing of rivers into the ocean, and so on. in themore than two thousand years since his discovery, the watermolecules from archimedes' bathwater have been through this cycleenough times that they are probably about evenly distributedthroughout all the water on the earth. when you buy a can of soda, about how many molecules from that famous bathtub of archimedes arethere in that can?


The answer is water molecules are split.cellular respiration and photosynthesis are complement  reactions to each other. these are reverse reactions. in cellular respiration glucose and oxygen yield water and carbon dioxide. so, when respiration begins,  glucose molecules are split. in the opposite reaction - in photosynthesis, carbon dioxide and water yield glucose and oxygen. thus,  when respiration begins, water molecules are split.

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.


8652.36857143 x 10^{4} molecules


We need a lot of assumptions in this case.

1. We don't know the mass of water that was present in Archimedes' bath tub that day.

2. Since it recycles, we don't know the total mass of water present on earth.

Assuming the total mass of water on earth is 1.4 × 10^{18} tonnes;

converting tonnes to kgs -->>  1.4 × 10^{21}kg

Since only 2.5% of this is fresh, (the rest is saline and ocean-based)

-->> 2.5% of 1.4 × 10^{21}kg = 0.035  × 10^{21}kg

An average bath tub holds about 80 gallons of water.

80 gallons to kgs = 302.8329 kg

Using Avogadro's number,

we have about 6 × 10^{23} molecules in 18g of water;

1kg of water would contain about 3.3 × 10^{25} molecules.

An average water can holds about 355mL of fluid.

Therefore the number of molecules in the can is 10^{25}.

The number of bathtub molecules present in the can is;

302.8329 x 10^{25} / 0.035 x 10^{21}

= 8652.36857143 x 10^{4} molecules

Do you know the answer?

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