A famous physicist asserts that the following story is true. You are to argue wh
ID: 1886169 • Letter: A
Question
A famous physicist asserts that the following story is true. You are to argue whether or not the assertion is correct based on your estimate and reasoning. 2. Once upon a time an American traveler in Italy returned to her hotel room after a vigorous night at the opera. Seeking to quench her thirst she drew a glassful of water from the tap. At the first sip she noticed a suspicious "off-taste" in the water and so, having flung the window open, she cast the water out into the Adriatic Sea below. Her travels in Europe continued for "sufficient time" that the water which had originally been in the glass was now "well mixed in all the oceans of the world. Upon returning to Santa Cruz our physicist was so overjoyed to behold her native land again that she took out a glass and filled it from the Monterey Bay. Little did she know that there were millions of atoms in that second glass of water which had originally been in that first glass of bad water she had tossed out in Italy. (continued)Explanation / Answer
Let's first understand what the assertion says. It says that the new glass contained millions of atoms from the first glass. For that we will have to do the following calculations
1. Calculation of water in the world
V = A x d
A = 0.7 x 4 x 3.14 x R^2 .... Because 70% of earth surface is water
= 0.7 x 4 x 3.14 x (6.4 x 10^6)^2 = 3.6 x 10^14 m2
V = A x d = 3.6 x 10^14 x 4000 = 1.44 x 10^18 m3
2. Calculation of world water in terms of glasses
1 glass = 200ml = 0.2 litre = 0.2 x 10^-3 m3
no. of glass = V/Vglass = 7.2 x 10^21 glasses
3. No. of atoms in a single glass of water.
1 glass = 200 gms = 200/18 = 11.11 moles of water = 11.11 x 6.023 x 10^23 = 6.7 x 10^24 molecules
= 6.7 x 10^24 x 3 atoms = 2 x 10^25 atoms.
4. Assuming the atoms from the first glass were uniformly spread around the world, each new glass will contain
No. of atoms in new glass = No. of atoms in original glass / No. of glasses in the world
= 2 x 10^25 / 7.2 x 10^21 = 2778 atoms
This means that any new glass would on an average have only about 2778 atoms from the older glass. Hence, the assertion of the physicist (saying million same atoms) is wrong.
He is off by a factor of 10^3. Hence, even if we increase the depth of ocean by a factor of 10^3, the conclusion won't change.
upvote if it helped
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.