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STALIN [3.7K]
2 years ago
7

Enrico Fermi (1901–1954) was a famous physicist who liked to pose what are now known as Fermi problems, in which several assumpt

ions are made in order to make a seemingly impossible estimate. Probably the most famous example is the estimate of the number of piano tuners in Chicago using the approximate population of the city and assumptions about how many households have pianos, how often pianos need tuning, and how many hours a given tuner works in a year. Another famous example of a Fermi problem is "Caesar's last breath," which estimates that you, right now, are breathing some of the molecules exhaled by Julius Caesar just before he died. The assumptions made are: The gas molecules from Caesar's last breath are now evenly dispersed in the atmosphere. The atmosphere is 50 km thick, has an average temperature of 15 °C , and an average pressure of 0.20 atm . The radius of the Earth is about 6400 km . The volume of a single human breath is roughly 500 mL . Perform the calculations, reporting all answers to two significant figures.
Physics
1 answer:
Katarina [22]2 years ago
5 0

Answer:

Explanation:

(a)

Since the earth is assumed to be a sphere.

Volume of atmosphere = volume of (earth +atm osphere) — volume of earth

= \frac{4}{3}\pi(6400+ 50)^3 -  \frac{4}{3}\pi (6400)
^3\\\\=  \frac{4}{3}\pi(6192125000) km’^3\\= 2.6\times 10^{19} m^3

Hence the volume of atmosphere is 2.6\times 10^{19} m^3

(b)

Write the ideal gas equation as foll ows:

PV = nRT\\\\n\frac{0.20atm\times 2.6\times10^{19} m^3}{0.08206L\, atm/mok\, K \times (15+273+15)K}\times \frac{1L}{10^{-3}m^3}\\\\= 2.20\times 10^{20} moles

no.\, of\, molecules = 2.20\times 10^{20} moles \times \frac{6.022\times10^{23}\,molecules}{1mole}= 13.3\times10^{43} molecules


Hence the required molecules is 13.3\times10^{43} molecules


(c)

Write the ideal gas equation as follows:

PV =nRT
\\\\n=\frac{1.0 atm \times 0.5L
}{0.08206 L\, atm/mol\,K \times (37 +273.1 5)K} = 0.0196 moles

no.\, of\, molecules = 0.0196 moles \times\frac{6.022\times10^{23} molecules}
{Imole}= 1.2\times 10^{23} molecules

Hence the required molecules in Caesar breath is 1.2\times 10^{23} molecules

(d)

Volume fraction in Caesar last breath is as follows:  

Fraction,\, X =\frac{12\times 10 molecules}{13.3\times 10^{43} \,molecules}= 9.0\times 10\, molecule/air\, molecule}

(e)

Since the volume capacity of the human body is 500 mL.

Volume\, of\, Caesar\, nreath\, inhale\, is =\frac{ 12\times 10^{22}\, molecules}{breath}\times \frac{9.0\times10^{-23} molecule}{air\, molecule}\\\\= 1.08 molecule/breath

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A disk with a radius of R is oriented with its normal unit vector at an angle Θ with respect to a uniform electric field. Which
marissa [1.9K]

Answer:

The expresion for the flux through the disk is:

Ф = E·πR^2·cos(Θ).

Explanation:

Let's sat the electric field has direction e and the normal to the disk has direction n (bold means vector quantities). So we have:

E=E·e (where E is the magnitud of the electric flied)

A=A·n

The flux for an uniform electric field and a flat surface is:

Ф=E×A

⇒ Ф = E·A·e×n = E·A·cos(angle(e,n)) = E·A·cos(Θ)

Since in this case the area is for a disk of radius R, A=\pi R^{2}

So, Ф = E·πR^2·cos(Θ)

8 0
3 years ago
Read 2 more answers
A .025 kg bullet is moving at 350 m/s when it hits and then passes through a 7 kg block of wood. After the bullet passes through
slamgirl [31]

Answer:

The final velocity of the wooden block is equal to 1.035 m/s

Explanation:

Given that mass of bullet = m_{b} = 0.025kg

                Mass of wood = m_{w} = 7kg

               Initial velocity of bullet = u_{b} = 350m/s

              Final velocity of bullet = v_{b} = 60m/s

               Initial velocity of wood = o

               Final velocity of wood = v_{w]

   Here momentum is conserved so initial momentum = final momentum

            m_{b}u_{b} = m_{b} v_{b} + m_{w}v_{w} .

    Upon substituting these values in above equation , we get

        v_{w} = 1.035m/s.

7 0
3 years ago
Newton’s second law of motion addresses the relationship between what two variables that influence the force on a body?
IgorC [24]

Newton’s Second Law concerns the generation of force based on an object’s mass and acceleration, as described by the equation F=ma.

Hope this helps!

8 0
3 years ago
Read 2 more answers
1. A runner has an initial speed of 2 [m/s] and slowly speeds up with a constant acceleration of
zvonat [6]

Answer:

Final Velocity = 4.9 m/s

Explanation:

We are given;. Initial velocity; u = 2 m/s

Constant Acceleration; a = 0.1 m/s²

Distance; s = 100 m

To find the final velocity(v), we will use one of Newton's equations of motion;

v² = u² + 2as

Plugging in the relevant values to give;

v² = 2² + 2(0.1 × 100)

v² = 4 + 20

v² = 24

v = √24

v = 4.9 m/s

5 0
2 years ago
In a high school swim competition, a student takes 1.6 s to complete 1.5 somersaults. Determine the average angular speed of the
Rufina [12.5K]

Answer:

The  angular speed is w = 5.89 \ rad/s

Explanation:

From the question we are told that

    The time taken is  t = 1.6 s

    The number of somersaults  is n  =  1.5

The total angular displacement during the somersault is mathematically represented as

         \theta  =  n *  2 *  \pi

substituting values

        \theta  =  1.5 *  2 *  3.142

       \theta  = 9.426 \ rad

 The angular speed is mathematically represented as

         w =  \frac{\theta }{t}

substituting values

         w =  \frac{9.426}{1.6}

          w = 5.89 \ rad/s

     

3 0
3 years ago
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