A spherical bulb 10 cm in radius is maintained at room temperature (300 K) except for one square centimeter which is kept at liquid nitrogen temperature (77 K). The bulb contains water vapor originally at a pressure of 0.1 mmHg. Assuming that every water molecule striking the cold area condenses and sticks to the surface, estimate the time required for the pressure to decrease to 10^-4 mmHg. [Assume that the gas remains in equilibrium at 300 K, but keeps losing molecules because of the " effusion" of molecules that hit the 1 cm^2 cold patch.]

Answers

Answer 1

The time required for the pressure to decrease to 10⁻⁴ mmHg is approximately 0.7 x 10⁵ s.

The rate at which water vapor molecules hit the cold patch and condense can be calculated using the kinetic theory of gases.

The number of water vapor molecules per unit volume in the bulb can be approximated by the ideal gas law:

PV = nRT

where,

P = pressure,

V = volume,

n = number of molecules,

R = gas constant, and

T = temperature.

Solving for n/V, we get:

n/V = P/RT

Given, P = 0.1 mmHg = 0.1/760 atm

           T = 300 K

Therefore, number of water vapor molecules per unit volume is:

n/V = (0.1/760 atm) / [(8.31 J/mol K) (300 K)]

      = 5.28 × 10⁻⁸ mol/m³

      = 5.28 × 10⁻⁸ * (6.02 x 10²³ molecules/mol)

      = 3.18 ×10¹⁶ molecules/m³

The rate at which water vapor molecules effuse through the cold patch can be approximated using Graham's law of effusion:

[tex]\frac{r_{1}}{r_{2}} =\sqrt{\frac{M_{2} }{M_{1} } }[/tex]

where rate1 and rate2 are the rates at which two gases effuse through a small hole, and M1 and M2 are their molecular masses.

In given condition,

we can treat the water vapor molecules as effusing through the cold patch into a vacuum,

∴ rate = A* (1/4) * (n/V) * √(8kT/πm)

where, A is the area of the cold patch, k is the Boltzmann constant, T is the temperature, and m is the mass of a water molecule.

Substituting the values, we get:

rate = 1 × 10⁻⁴ * (1/4) * (3.18×10¹⁶) * √[(8 * 1.38x10⁻²³ * 300) / (π * 3.01x10⁻²⁶)]

      = 1 × 10⁻⁴ * (1/4) * (3.18×10¹⁶) * 0.59

      = 4.69 x 10¹³ molecules/s

This is the rate at which water vapor molecules are removed from the bulb. The time required for the pressure to decrease to 10^-4 mmHg can be approximated by assuming that the pressure decreases exponentially with time:

P(t) = P₀ exp(-kt)

where P₀ is the initial pressure, k is a constant, and t is the time.

The constant k can be calculated from the rate:

k = rate / N

where N is the number of water molecules per unit volume.

Substituting the values, we get:

k = 4.69 x 10¹³ molecules/s / 3.18 ×10¹⁶ molecules/m³

k = 1.47x 10⁻³ s⁻¹

The time required for the pressure to decrease to 10⁻⁴ mmHg can then be calculated:

10⁻⁴ mmHg = 0.1 mmHg  exp(-1.47x 10⁻³ * t)

∴ t = 0.7 x 10⁵ s

Therefore, the time required for the pressure to decrease to 10⁻⁴ mmHg is approximately 0.7 x 10⁵ s.

Learn more about pressure here

brainly.com/question/26822196

#SPJ4


Related Questions

A force of 10 N acts to the left and a force of 5 N acts to the right on an object of mass 1 kg. If its initial speed is zero , what is its velocity after 1 second ?

Answers

Answer: -5 m/s

Explanation:

First find the net force by summing up the forces:

-10N + 5N = -5N

Use Newton's Second Law of motion to solve for the acceleration:

F = ma

-5N = 1kg(a)

a = -5 m/s^2

Use the first kinematic equation to solve for the final velocity:

Vf = Vi + at

Vf = 0 + (-5)(1)

Vf = -5 m/s

What is the main reason people and bears slip and fall on ice, be careful when outside in the snow/ice.

Answers

Answer:

Both ice and snow have a lower coefficient of friction in comparison with grass, wood or pavement.

Explanation:

The main reason why people and bears, slip and fall on ice/snow is that both ice and snow have a lower coefficient of friction in comparison with grass, wood or pavement. We present below a comparative chart of coefficients of friction associated with different materials:

Material       Coefficient of Friction - Static                  

Ice/Snow                   0.05 - 0.3

Wood                          0.2 - 0.6

Asphalt                        0.5 - 0.7

Grass                            0.3 - 0.5

What is the kinetic energy of a 5kg ball that is rolling 3m/s?

Answers

Answer:

22.5

Explanation:

As the mass is 5 kg,velocity is 3m/s so the derivation use for kinetic energy is 1÷2 mv*2 . By this derivation we will find out the kinetic energy

the organelles are giving their job description to you can you identify which organelle are they? write your answers in your answer sheet.
1. Hi! My responsibility is to add stability and protection to plant cells. What am I?
2. Hi! produce proteins inside the cell. What am I ?
3. Hello! I have a green pigment called the clorophyll. I also absorb solar energy to do the process of photosynthesis. What am I?
4. Good morning po! my work is to store food materials and excretes waste materials. I take a large space on plants. I make the leaves of plants fresh. what am i?
5. Hi! All organelles are embedded in me. I am a "jelly- like" substance. What am I?
Please real answer ​

Answers

1. cell wall?

2. ribosomes?

3. chloroplast

4. vacuoles

5. cytoplasm

what type force does this depict?

Answers

Answer:

c. gravitational force

Explanation:

percent of Earth's surface is made up of Oxygen.
a) 30
b) 46
c) 62

Answers

Answer: it's made up about 21% so if you do not have this option I say go with 30

Explanation:

Select the correct answer.
Which pair of atoms has the highest electronegativity difference?
OA.
H-S
B.
H-Cl
o c.
N-H
OD.
О – Н
O E.
C-H

Answers

Answer:O – H

Explanation:

what are common in the pictures?​

Answers

Answer:

the flowers the left have them on there heads the middle on there chest and the right one has them on there shoulders

the force required to lift a load of 800 Newton by using a Lever having a mechanical advantage of 1.6 is​

Answers

Answer:force required to lift the load = 500N

Explanation:

Mechanical advantage for a lever is given by the formulae

= force output/force input

or

Mechanical Advantage = Load / Effort

where

Force output  / Load= 800 N

mechanical advantage = 1.6

Force input / Effort =??

Force input=  Force output /Mechanical advantage

= 800N / 1.6

=500N

OR

Effort = Load/ Mechanical Advantage = 800/ 1.6 = 500N

A rock with a mass of 80grams dropped into a graduated cylinder with 30 ml of water in it the readingof water became 70 ml what is the density of the rock

Answers

Explanation:

[tex]b = m \div v \\ 80 \div 30 \times 10 { -}^{2} [/tex]

give three example what are the aims of each team in playing basketball?​

Answers

Answer:

The main objective of basketball is to make a goal and score points.Each team should not only try to make a goal and prevent the opposite team from taking control of the ball, but should also try to protect the basket in their court and prevent the opponent from making a goal.

hope that helps..

A tractor pulls a 1,000 kg wagon with a force of 4,000N. What is the wagon’s acceleration in m/s2? *

Answers

Answer:

4m/s^2

Explanation:

acceleration=force/mass

therefore a=4000/1000

=4m/s^2

How are the sun and Earth's moon different?(2 points)
The sun is a ball of gases that revolves around Earth, while the moon is the center of the solar system,
The sun is a ball of rock and gas, while the moon is a ball of rock that revolves around the sun.
The sun is the center of the solar system, while the moon is a ball of rock that revolves around Earth
The moon is the center of the solar system, while the sun is the center of the Milky Way.

Answers

Answer: The Sun measures 1.4 million km across, while the Moon is a mere 3,474 km across. In other words, the Sun is roughly 400 times larger than the Moon. But the Sun also happens to be 400 times further away than the Moon, and this has created an amazing coincidence.

Explanation:


what is the wavelength of the wave

Answers

Explanation:

it is equal to the speed (v) of a wave train in a medium divided by its frequency (f): λ = v/f. Waves of different wavelengths.

Answer:

It is measured in the direction of the wave. Description: Wavelength is the distance from one crest to another, or from one trough to another, of a wave (which may be an electromagnetic wave, a sound wave, or any other wave).

This tasty snack starts as a kernel and is “popped” then
covered in salt, butter, caramel, peanuts, you name it.
Through thermal energy we've learned to heat things, you
could use conduction, convection and/or radiation. Describe
1 cooking option in detail including whether it is convection,
conduction or radiation. Must be at least 2 sentences.

Answers

Popcorn can be popped by either of the three forms of heat transfer:

Conduction in a pan with hot oil on a stove element.

Convection by an air popper and warm air rising over a heating element... no direct contact with heat source.

Radiation is what occurs in a microwave. Invisible radiant heat activates water molecules in the popcorn.

All the above heat the kernel over 100 Celsius. Water vaporizes/boils (latent heat) and erupts through the kernel.

Mmmm popcorn watch out for the lipids (fat in the oil and butter)

A rocket at rest with a mass of 942 kg is acted on by an average net force of 6,731 N upwards for 21 s. What is the final velocity of the rocket?

Answers

Answer:

Final velocity, V = 150.15 m/s

Explanation:

Given the following data;

Mass = 942kg

Net force = 6,731N

Time = 21secs

To find the final velocity of the rocket;

First of all, we would determine the acceleration of the rocket with respect to time.

Force = mass * acceleration

Substituting into the equation, we have;

6,731 = 942*acceleration

Acceleration = 6731/942

Acceleration = 7.15m/s²

Now, to find the final velocity we would use the first equation of motion.

V = U + at

Since the rocket started from rest, its initial velocity (U) is zero.

V = 0 + 7.15*21

Final velocity, V = 150.15 m/s

plzz helpppp meee!!!!

A farmer cannot get his cow to move without help. The cow has a mass of 425 kg. He returns with some neighbors, and they are able to exert a net force of 900 N on the cow. What is its acceleration?​

Answers

A=f/m
A=900/425
A=2.18

To determine acceleration you divide the force by the mass.

Answer:

hhh

Explanation:

What is the direction of the current in the loop as the north pole of the magnet is pulled away (to the right) from the loop of wire. Answer as you face the loop from the magnet.

Answers

Answer:

Explanation:

Applying Fleming's right hand rule, the induced current would flow in a clockwise direction in the loop. Explanation: Current, magnetic field and motion are mutually dependent and perpendicular to one another.Aug 27, 2019

Energy is defined as ____________.

The ability of an object to produce a change in the environment or itself

motion

the effort required to perform work

power

Answers

Answer:

The effort required to perform work

Explanation:

One of the largest planes ever to fly, and the largest to fly frequently, is
the Ukrainian-built Antonov An-124 Ruslan. Its wingspan is 73.2 m
and its length is 69.2 m. The gravitational potential energy associated
with the plane at an altitude of 1.45 km is 3.36 x 10^9 J. What is the airpanes mass

Show work pls :)

Answers

The gravitational potential energy associated with the plane is 2.36 x [tex]10^{5}[/tex] J

What is gravitational potential energy?

Gravitational potential energy is energy an object possesses because of its position in a gravitational field.

It is given by P.E = mgh

where m = mass

g= acceleration due to gravity

h = height of the object

Here,

h = 1.45km  = 1450 m

P.E = 3.36 x [tex]10^{9}[/tex] J

g = 9.8m/[tex]s^{2}[/tex]

therefore, m = P.E/ gh = (3.36 x [tex]10^{9}[/tex]s J)/ 9.8 x 1450

m = 2.36 x [tex]10^{5}[/tex]

Hence mass of the airplane is 2.36 x [tex]10^{5}[/tex]

To know more about gravitational potential energy here

https://brainly.com/question/19768887

#SPJ2

How many total molecules are present in the formula below
2H2O

Answers

There are 4 in there I believe

I'm guessing 6.

the coefficient of two turns our hydrogen into 4 and our oxygen into 2 which makes a total of 6 molecules.

how do I write an essay on how I feel about online school​

Answers

Answer:

Some students appreciated the social aspect of Zoom classrooms, while others felt online education worked best for them when they were working on their own. ... Students said they appreciated having a well-planned work week and didn't appreciate “surprise” assignments online any more than they appreciate them in class

Explanation:

What's I know I said

What do you u write it

Una pieza de platino metalico con densidad 21.5 g/cm3 tiene un volumen de 4.49 cm3. Cual es su masa

Answers

Answer:

m = 96.53 grams

Explanation:

Given that,

The density of metallic platinum, d = 21.5 g/cm³

Volume, V = 4.49 cm³

We need to find the mass. Let it is m. We know that the density is equal to the mass per unit volume. So,

[tex]d=\dfrac{m}{V}\\\\m=d\times V\\\\m=21.5\times 4.49\\\\m=96.53\ g[/tex]

So, the required mass is 96.53 grams.

Importance of Forest ​

Answers

Answer:

to help keep fresh air

Explanation:

To produce oxygen and protect oxygen

Complete the sentence. Friction always ____________

a. helps the motion

b. opposes the motion

c. both of these

d. none of these

Answers

Answer:

B- Opposes the motion

Explanation:

When two object touches each other. friction acts in a opposite direction to the motion of the object

B. Opposes the motion.

A marble rolling across a flat surface will not roll forever. This is due to friction. The marble rubs against the flat surface, slowing down until it finally stops.

Two spheres are moving towards each other. Which of the following is the
best evidence that the spheres have transferred energy from one to the other?

A.The friction of the surface decreases

B.Gravity is always acting on the spheres

C.The motion of the sphere changes

Or

D.Both of the spheres have the same mass

Answers

Answer:

D

Explanation:

If they are both moving at the same speed then its D.

plsss anyone help I BEG. its not that hard im just lazy and don't feel like thinking3

Answers

Answer:

Well I think you should think

Motion Quiz 1
Part I. Vocabulary (5 points each)
1. The location of an object.
2. A change in the position of an object in reference to a starting point. 3. A change in the position of an object that includes distance and direction. 4. North, south, right, and down are all examples of ________. 5. How fast or slow something moves over a given distance per unit of time. 6. A unit of measurement for time.
Part II. Multiple Choice (10 points each)
Direction
Displacement Meters
Minutes
Motion
Position
Speed

A toy robot moved from a starting point, traveling in a straight line at different speeds and then turning around and returning to the starting point at different speeds.

7. What is the total distance that the toy robot traveled?
A. 12 m
B. 24 m
C. 48 m
D. 96 m
8. A cyclist travels 3 km north in 25 minutes. What does this information describe?
A. mass
B. force
C. motion
D. gravity
9. A book is lying on a seat in a car that is moving at 50 kilometers per hour (km/h). The driver says that the book is not moving. An outside observer says the book is moving at 50 km/h because it is in the car. Which is the most logical conclusion for these two statements?
A. Motion is detected only if the car accelerates and is measured by the observer.
B. Motion is absolute, and the driver is incorrect saying that the book has no motion.
C. Motion is relative to a given frame of reference, and both the driver and observer are correct.
D. Motion is constantly changing so neither person’s statement will be correct when the car slows down.
10. Which measurement describes the speed of a rubber ball?
A. 5 cm
B. 10 m/s
C. 15 newtons
D. 50 grams
11. A change in the position of an object as time changes best describes
A. direction.
B. waves.
C. motion.
D. frequency.
12. A school bus moves past a parked car at a speed of 30 km/h. Which of the following best describes the observation made by a passenger on the bus?
A. The car appears to be moving 30 km/h in the same direction as the bus.
B. The car appears to be moving 30 km/h in the opposite direction of the bus. C. The car appears to be moving 15 km/h in the same direction as the bus.
D. The car appears to be moving 15 km/h in the opposite direction of the bus.
13. Calculate the speed when the distance travelled is 800 km and the time is 40 seconds. A. 200 km/sec
B. 320 m/sec
C. 20 km/sec
D. 32 m/sec

Answers

Do you still need help with this question

calculate the change in gravitational potential energy of a stone of mass 0.55 kg as it falls through a distance of 2.7 m. ignore air resistance (mention formula)

Answers

Answer:

14, 85 J

Explanation:

The formula of potential Energy (P.E.) is

P.E. = m * g * h, where m is the mass in kilograms, g is the acceleration due to gravity (about 10 m / [tex]s^{2}[/tex] at the surface of the earth) and h is the height in meters.

Here P.E. is 0,55 kg * 10 m/s * 2,7 m = 14, 85 J

Two photographers are competing for business in town. Andrea uses only film photography and Keira uses only digital photography. Keira claims that the digital technology is superior, and her advertisement claims that the images can be stored, shared, and copied more easily. They can even be sent long distances using a series of wave pulses to transmit the information. Andrea replies that digital images can be stolen and altered more easily.
Do the advantages outweigh the disadvantages, or do both sides have valid points? Support your answer with at least three reasons

Answers

There is no right or wrong answer, your teacher wants you to support your own answer with points. As long as the reasons make logical sense you are fine.

I think they both have valid points. Their replies are both true, but from a buyer's perspective who would you purchase services from? You would get different answers depending on who you ask.

If you choose to go old school, obviously you get an actual photo that can be stored physically. This means it is a memory that can be preserved, and it might feel more nostalgic being able to touch the photo.

On the other hand, a digitally stored photo can be altered (photoshop), but it is forever as long as the internet still exists. A physical photo would fade with time, which doesn't happen with a digital photo.

It is definitely easier to argue that digital photography has more advantages (they do, it is why nobody uses film anymore)

Points you can consider:

Can be transferred to the other side of the world instantly

Ability to make copies and print as many photos as you want

Can be stored on cloud/devices and be like that forever

Compare them with film photography to give a more solid response.

Other Questions
Kawan buys some protein bars at $0.90 each and bottled water at $0.70 each for a group hike. He buys twice as many bottles of water as protein bars. If he spends $46 in total, how many bottles of water and protein bars does he buy? Let x= the number of protein bars A nurse is caring for a client who has poison ivy and dermatitis and is started on diphenhydramine (Benadryl). Which of the following nursing recommendations is appropriate for decreasing the dry mouth associated with the use of diphenhydramine The standard overhead applied is based on the ______ level of activity multiplied by the predetermined overhead rate. multiple choice question. standard actual budgeted Which of these may be integrated with an electronic stability control (ESC) system 5. A 12-ounce jar of jam costs $2.40. A 16-ounce jar costs $4.00. What is thedifference in the cost per ounce?$per ounce Rewrite the passive sentence 17. they don't help you. 18. he doesn't open the book. How many grams of Aspirin (acetylsalicylic acid) should we form in this reaction if we started with 2.08g of Salicyclic Acid? Darker colored rocks that are rich in iron and magnesium are are referred to as being ____________________ in composition. I need a good answer, with a good explanation. Janie and Jasmine are playing three games at an arcade. Each of the games requires either 2, 3, or 4 tokens. The girls plan to play as many games as they can before running out of tokens.Write an expression to represent the total number of tokens that Janie and Jasmine will need to play each of the three games at least once. Let m represent the number of games that require 2 tokens; n represent the number of games that require 3 tokens; p represent the number of games that require 4 tokens. What is the generic name of this molecule? (Ph stands for phenyl) Noah drops a rock with a density of 1.73 g/cm into apond. Will the rock float or sink? Explain your answer. What was the primary reason for the writing of this document? to create an international organization based on collective security to enforce the protection of human rights by member nations to nullify previous international treaties and security agreements to establish an international economic fund to support war refugees Which function is graphed? Write an expression, of the type A log(x B), for the transformed logarithmic function shown below: The event described in the headline happened because President Andrew Jackson: A-blamed the National Bank for causing an economic panic. B-thought the National Bank should issue more paper money. C-believed the National Bank favored the wealthy.D-wanted the National Bank to set up new tariffs. The Treaty of Versailles made four major demands of Germany following World War I. Of the four below, which two had the most profound economic impact on the country If an electric dryer has a nameplate rating of 5.6kva what would you use for the service calculation? Zebulon Pike Explored lands in Texas that were unknown to most Americans and were not yet a part of US territory which reason explains why his explorations were important? Write the definition in your own wordsCash Basis of Accounting: Accrual Basis of Accounting:Matching Principle:Time-Period Principle: Accounting Period: Help ASAP!!! Geometry, fill in the blanks