The Third Law of Thermodynamics states that as the temperature of a system approaches absolute zero, the entropy of the system approaches a minimum value.
Entropy is a thermodynamic quantity that measures a system's degree of disorder or unpredictability. The higher the entropy of a system, the more disorganised or unpredictable it is. According to the Third Law of Thermodynamics, the entropy of a system at absolute zero is the lowest value that can be achieved.
The Third Law of Thermodynamics and entropy are intimately related since the Third Law limits a system's entropy. The Third Law states that as a system approaches absolute zero, its entropy approaches a minimum value, which is specified by the Third Law.
The Third Law also suggests that reaching absolute zero temperature is unachievable, and so the minimal entropy is an unattainable goal.
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why is using dry nitrogren or argon a suitable environemtn for a grignard reaction
Using dry nitrogen or argon is a suitable environment for a Grignard reaction because these gases are inert and do not react with the reagents used in the reaction.
What is the Grignard reaction?
A Grignard reagent is an organometallic compound formed by reacting an organic halide with magnesium metal. A Grignard reaction is a chemical reaction that occurs between an organic halide (R-X) and a Grignard reagent (R'-MgX), forming a new carbon-carbon bond. This reaction is an essential tool in organic synthesis because it can be used to form a wide range of organic compounds.
Nitrogen or argon gas in Grignard reaction:
The reaction is highly sensitive to water, which can quickly destroy the Grignard reagent, and therefore the reaction must be performed under a dry atmosphere. Using dry nitrogen or argon is a suitable environment for a Grignard reaction because these gases are inert and do not react with the reagents used in the reaction. They help to maintain the dry atmosphere required for the reaction to take place without any unwanted side reactions. Additionally, these gases help to prevent the reaction from oxidizing, which can result in the production of unwanted byproducts.
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Give an example of a positively charged object
only a relatively small part of the electromagnetic spectrum is visible. what determines which bands of the electromagnetic spectrum are invisible to humans?
Answer:
hsnzbssj
Explanation:
skibbbbbbbbbbbbibiA Toddler got up from a nap and ran for 7.0 seconds and got tired and stopped on the spot. from beginning to end she was accelerating at 0.24m/s^2. What has her change in velocity in metres per second
The toddler's change in velocity in metres per second is 1.68 m/s
To answer the question, we need to know what acceleration is
What is aceleration?Acceleration is the change in velocity of an object with time. It is given by
a = Δv/Δt where
Δv = change in velocity and Δt = change in time The toddler's change in velocityMaking Δv subject of the formula, we have
Δv = aΔt
Since the toddler's accleration is 0.24 m/s² and got up from a nap and ran for 7.0 seconds,
a = 0.24 m/s² and Δt = 7.0 sSubstituting the values of the variables into the equation, we have
Δv = aΔt
Δv = 0.24 m/s² × 7.0 s
Δv = 1.68 m/s
So, the toddler's change in velocity in metres per second is 1.68 m/s
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A dart is fired horizontally from a dart gun, and
another dart is dropped simultaneously from the
same height. If air resistance can be neglected,
which dart hits the ground first?
Both the darts hits the ground at the same time, because acceleration is the same.
Why is air resistance a force?
Italian physicist Galileo Galilei, who is extremely well-known, discovered air resistance. He climbed to the top of the Leaning Tower of Pisa and threw numerous articles from the height.When an object moves through air, air creates a force known as air resistance. A body moving through the air will experience this force acting in the opposite direction. The moving body is frictionally forced against by air resistance. Air resistance slows a body down as it moves.A moving body's direction can be changed by air resistance, which has both strength and direction.The air resistance asserts that the air density () determines the force's size. The average value for this is 1.2 kg/m3.To learn more about air resistance refer to:
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Johann squeezes a bagel too hard at the supermarket, and it does not return to its original shape when he removes his hand. The bagel has been __________ deformed. What word completes the sentence to show that the bagel has been permanently changed?
Answer:
permanent set
.............
Johann squeezes a bagel too hard that it is not able to return to its original shape. The bagel has Plastic deformation.
What is Plastic Deformation?Plasticity, also referred to as plastic deformation, is the property of a solid material to undergo permanent deformation, a non-reversible change in shape in response to applied forces.
It is a concept used in physics and materials science. For instance, plasticity is demonstrated when a solid piece of metal is bent or pounded into a new shape because the material itself undergoes lasting modifications. Engineering professionals use the term yield to describe the change from elastic to plastic behavior.
Most materials, especially metals, soils, rocks, concrete, and foams, show signs of plastic deformation.
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A student walked 100 meters North, then 100 meters West. How many more meters did the student walk compared to their total displacement from their starting point?
A. The total distance walked is about 71 meters less than the student’s displacement.
B. The total distance walked is double the magnitude of the student’s displacement.
C. The total distance walked is about 59 meters more than the student’s displacement.
D. The total distance walked is equal to the magnitude of the student’s displacement.
Answer:
C. The total distance walked is about 59 meters more than the student’s displacement.
Explanation:
The total distance walked is equal to the magnitude of the student’s displacement is the correct option. The correct answer is (D).
The student walked 100 meters North.
Then, the student walked 100 meters West.
Total distance walked = √(North distance)² + (West distance)²
Total distance walked = √(100)² + (100)²
Total distance walked = √(10000 + 10000)
Total distance walked = √20000
Total distance walked = 141.42 meters
Displacement = √(North distance)² + (West distance)²
Displacement = √(100)² + (100)²
Displacement = √(10000 + 10000)
Displacement = √20000
Displacement = 141.42 meters
The student's total distance walked is 141.42 meters, and their displacement is also 141.42 meters.
The total distance walked to the displacement:
Total distance walked = 141.42 meters
Displacement = 141.42 meters
So, the correct option is D) The total distance walked is equal to the magnitude of the student’s displacement.
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what does a blue shift in light from stars indicate?
Answer:
If a star is moving towards the earth, its light is shifted to higher frequencies on the color spectrum (towards the green/blue/violet/ultraviolet/x-ray/gamma-ray end of the spectrum). A higher frequency shift is called a "blue shift".
Explanation:
It just means that the entire spectrum is shifted up in frequency.
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 7.0 parts/million (ppm). A researcher believes that the current ozone level is at an insufficient level. The mean of 1080 samples is 6.9. Assume the standard deviation is known to be 1.1. Does the data support the claim at the 0.02 level? Step 3 of 5 : Specify if the test is one-tailed or two-tailed. Answer 2 Points Keyboard Shortcuts One-Tailed Test Two-Tailed Test Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 7.0 parts/million (ppm). A researcher believes that the current ozone level is at an insufficient level. The mean of 1080 samples is 6.9 ppm. Assume the standard deviation is known to be 1.1. Does the data support the claim at the 0.02 level? Step 1 of 5: Enter the hypotheses: Answer 2 Points Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 7.0 parts/million ( ppm ). A researcher believes that the current ozone level is at an insufficient level. The mean of 1080 samples is 6.9ppm. Assume the standard deviation is known to be 1.1. Does the data support the claim at the 0.02 level? Step 2 of 5: Enter the value of the z test statistic. Round your answer to two decimal places. Answer How to enter your answer (opens in new window) 2 Points Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 7.0 parts/million (ppm). A researcher believes that the current ozone level is at an insufficient level. The mean of 1080 samples is 6.9 ppm. Assume the standard deviation is known to be 1.1. Does the data support the claim at the 0.02 level? Step 5 of 5 : Enter the conclusion. Answer 2 Points Keyboard Shortcuts Reject Null Hypothesis Fail to Reject Null Hypothesis Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 7.0 parts/million (ppm). A researcher believes that the current ozone level is at an insufficient level. The mean of 1080 samples is 6.9 ppm. Assume the standard deviation is known to be 1.1. Does the data support the claim at the 0.02 level? Step 4 of 5 : Enter the decision rule. Answerhow to enter your answer (opens in new window) 2 Points Keyboard Shortcuts Reject H 0
if z
Assuming that the standard deviation is known to be 1.1, for a mean of 1080 samples, it can be said that the data supports the claim that the current ozone level is insufficient at the 0.02 level.
Step 1 of 5: Enter the hypotheses:
Null hypothesis (H0): The current ozone level is sufficient (μ = 7.0 ppm)
Alternative hypothesis (H1): The current ozone level is insufficient (μ < 7.0 ppm)
Step 2 of 5: Enter the value of the z-test statistic:
To find the z-test statistic, we'll use the formula:
z = (X' - μ) / (σ / √n)
where:
X' = sample mean = 6.9 ppm
μ = population mean = 7.0 ppm
σ = standard deviation = 1.1 ppm
n = sample size = 1080
Substituting the values into the formula:
z = (6.9 - 7.0) / (1.1 / √1080)
z = -0.1 / (1.1 / 32.863)
z ≈ -0.1 / 0.033157
z ≈ -3.018
Step 4 of 5: Enter the decision rule:
Since the alternative hypothesis is one-tailed (μ < 7.0 ppm), we need to compare the z-test statistic with the critical value for the given significance level.
At a significance level of 0.02, the critical value can be found using a z-table or a calculator. For a one-tailed test, the critical value is approximately -2.055.
Step 5 of 5: Enter the conclusion:
The z-test statistic (-3.018) is smaller than the critical value (-2.055). Therefore, we reject the null hypothesis.
Conclusion: The data supports the claim that the current ozone level is insufficient at the 0.02 level.
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electrostatic precipitators use electrical charges to attract and track what pollutants?
Electrostatic precipitators use electrical charges to attract and trap pollutants, such as dust particles, sulfur dioxide, and smoke particles.
This technology works by using high voltage to ionize the pollutant particles, which changes their electrical charge and results in an attractive electrical force that is directed to metal plates or tubes, known as collectors.
Once the particles reach the collector, they build up and can be removed from the air. This technology is usually used to control emissions of particles that are too small to be blocked by traditional mechanical filters, such as those found in large power plants and fossil fuel facilities.
Because electrostatic precipitators are so efficient and powerful, they are now frequently used in many industries where air pollution control is needed. With proper maintenance and upkeep, this technology can be very effective in reducing air pollution, and keeping the surrounding air clean.
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Was there a difference in the conduction velocity measured on the median nerve in the arm and using the ankle reflex in the leg? what factors might contribute to a difference?.
A cell that is dedicated to the transmission of nerve impulses is known as a neuron. The axon, which is typically a lengthy protrusion or process that transfers impulses away from the cell body of a neuron toward target cells, is the portion of the neuron that transmits impulses.
The signal sent along an axon by nerve cells that enables them to interact and activate several systems in an organism is known as a nerve impulse, also known as an action potential.
An action potential may start in the brain and lead to a conscious movement, or it may be a part of a reflex arc that is not controlled by the brain. A muscle cell may receive an action potential, leading to muscular contraction.
Neurons are able tohaving the ability to produce action potentials. A change in the permeability of the neuronal membrane results in the action potential.
The induced action potential is transported up the leg to the spinal cord and back down where it causes the gastrocnemius (calf) muscle to contract when the Achilles tendon is extended after being tapped with a reflex hammer.
The Reflex Arc: When a tendon is stretched, the muscle's stretch receptors are activated, starting a reflex arc. These stretch receptors react by causing sensory neurons to go into action. These sensory neurons carry the action potential all the way to the spinal cord, where they make direct connections,
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Which of the following products will have elastic demand (alcohol, gasoline, travel souvenirs, cigarettes)
The product among alcohol, gasoline, travel souvenirs, cigarettes that will have elastic demand is cigarettes.
What is elastic demand?Elastic demand refers to a situation in which a change in the price of a good or service results in a more significant change in the amount demanded. When the percentage change in quantity demanded is greater than the percentage change in price, the demand for the product is said to be elastic.
When the quantity demanded of a product decreases significantly when the price rises, the demand for the product is said to be elastic. Similarly, when a slight change in price causes a significant change in quantity demanded, the demand is said to be elastic. Conversely, if a product's price increases by a small percentage, and the demand for the product decreases by a smaller percentage, the demand for the product is said to be inelastic.
Cigarettes, of all the products listed above, are likely to have an elastic demand.
This is because smokers who are addicted to cigarettes are more likely to quit smoking or reduce their consumption in response to an increase in the price of cigarettes compared to the other goods.
Thus, a slight increase in the price of cigarettes is likely to cause a significant decrease in the number of cigarettes consumed.
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What is the cutoff (threshold) frequency for a metal surface that has a work function of 5.42 eV? (1 eV = 1.60 × 10-19 J, h = 6.626 × 10-34 J ∙ s)
A) 1.31 × 1015 Hz
B) 2.01 × 1015 Hz
C) 3.01 × 1015 Hz
D) 5.02 × 1015 Hz
E) 6.04 × 1015 Hz
Explanation:
The cutoff (threshold) frequency for a metal surface that has a work function of 5.42 eV is given by the formula f0 = (φ/h) × (1/e),
where φ is the work function of the metal, h is the Planck's constant, and e is the charge of an electron.1
eV = 1.60 × 10-19 J, h = 6.626 × 10-34 J ∙ sHere,φ = 5.42 eV = 5.42 × 1.60 × 10-19 Jh = 6.626 × 10-34 J ∙ se = 1.60 × 10-19 C
Thus, the cutoff frequency is:f0 = (φ/h) × (1/e) = (5.42 × 1.60 × 10-19 J)/(6.626 × 10-34 J ∙ s) × (1/1.60 × 10-19 C)≈ 1.31 × 1015 Hz
Therefore, the cutoff (threshold) frequency for a metal surface that has a work function of 5.42 eV is 1.31 × 1015 Hz. The answer is A) 1.31 × 1015 Hz.
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which is the best example of an unbalanced force?
A)A book resting on a shelf
b)A train accelerating from the station.
c) A chair sitting motionless
d) a car driving at a constant speed.
plz answer correctly!!!!!
PLEASE HELPPPPP!!!!!!!!!
A circular loop of wire is placed in a uniform magnetic field directed out of the page. Suddenly the magnetic field disappear . What is the direction of the induced current in the loop?
Hi there!
Counterclockwise.
If a loop of wire is placed in a magnetic field directed out of the page that disappears, that means that the magnetic flux out of the page through the loop has decreased.
The loop will try to oppose this change in the magnetic flux, so an induced current that produces an additional magnetic field out of the page will occur to make up for the decrease in the magnetic flux.
Using the magnetic right-hand rule, the current in the loop would need to be traveling in the counterclockwise direction in order for the produced magnetic field to be directed out of the page inside the loop.
a balloon is rising at the constant rate of 5 meters per second a passes beneath it taveling in a straigthh line at the constant speed o10 meteres per second at the moment that the bicyclist is directly beneath the height of the balloon is 95 meters how fast is the distance between the and the balloon incrasing 5 seconds after the bicyclist was directly
Saying that someone or something is beneath you expresses your opinion that they are either unworthy of you or not appropriate for you.
What do you mean by beneath?They concluded that she should not marry. Alternatives: inappropriate, unworthy of, unsuited for, unsuitable for Additional Synonyms for below.
It is the passed beneath by which a velociraptor riding a bicycle while maintaining a steady speed of 6 meters per second. How quickly do the velociraptor's distances grow Under his T-shirt, she could make out the shoulders' muscles. Sitting beneath the trees gave her pleasure. The theatre's four levels of parking were insufficient.
He noticed that a known photo book on a shelf below. adverb further down than the; underneath; lower in the location than. close to the ground; short. below. underneath. bottom. bottommost the first drawer down from the top.
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When the Sun’s radiant energy falls on Earth’s oceans, it causes water to change state by evaporating. Which form of energy does water vapor have?
Answer:
water vapor is a type of gas
Explanation:
all gas are in air state of form
hope this helps
Answer:
chemical potential energy
Explanation:
When the sun's radiant energy falls on Earth's oceans, it causes water to change state by evaporating. The form of energy water vapor have is chemical potential energy. when heat energy of sun falls on water surface, its state change from liquid to gas. This gas rises above in the form of water vapor. Its a chemical change. If this vapor get condense/ cool, it will turn into liquid again. We can say that vapor has potential to transform into water again. Thus, the energy stored in water vapor is called chemical potential energy.
You want to lift a heavy box with a mass L = 64.0 kg using the two-ideal pulley system as shown. With what minimum force do you have to pull down on the rope in order to lift the box at a constant velocity? One pulley is attached to the ceiling and one to the box.
The given problem can be solved using the following free-body diagram:
The diagram is the free-body diagram for the pulley that is holding the weight. Where:
\(\begin{gathered} T=\text{ tension} \\ m=\text{ mass} \\ g=\text{ acceleration of gravity} \end{gathered}\)Now we add the forces in the vertical direction:
\(\Sigma F_v=T+T-mg\)Adding like terms:
\(\Sigma F_v=2T-mg\)Now, since the velocity is constant this means that the acceleration is zero and therefore the sum of forces is zero:
\(2T-mg=0\)Now we solve for "T" by adding "mg" from both sides:
\(2T=mg\)Now we divide both sides by 2:
\(T=\frac{mg}{2}\)Now we substitute the values and we get:
\(T=\frac{(64\operatorname{kg})(9.8\frac{m}{s^2})}{2}\)Solving the operations:
\(T=313.6N\)Now we use the free body diagram for the second pulley:
Now we add the forces in the vertical direction:
\(\Sigma F_v=T-F\)The forces add up to zero because the velocity is constant and the acceleration is zero:
\(T-F=0\)Solving for the force:
\(T=F\)Therefore, the pulling force is equal to the tension we determined previously and therefore is:
\(F=313.6N\)
Use Newton's method to find all solutions of the equation correct to six decimal places. (Enter your answers as a comma-separated list.) ln(x)=x−31 x=
The solution to the equation ln(x) = x - 31, correct to six decimal places, is x ≈ 24.662174.
Newton's method, also known as Newton-Raphson method, is an iterative numerical method used to find the roots of a real-valued function. It is a powerful algorithm for finding solutions to equations where it may be difficult or impossible to obtain an analytical solution.
To find the solutions of the equation ln(x) = x - 31 using Newton's method, we start by rearranging the equation to f(x) = ln(x) - x + 31 = 0.
Next, we need to choose an initial guess for the solution, let's say x0 = 20.
Then, we can use the Newton's method iterative formula:
xn+1 = xn - f(xn)/f'(xn)
where f'(x) is the derivative of f(x).
For our equation, f'(x) = 1/x - 1.
Let's perform the iterations:
x1 = x0 - (ln(x0) - x0 + 31) / (1/x0 - 1)
x1 = 20 - (ln(20) - 20 + 31) / (1/20 - 1)
x1 ≈ 24.660633
x2 = x1 - (ln(x1) - x1 + 31) / (1/x1 - 1)
x2 ≈ 24.662174
x3 ≈ 24.662174
Performing additional iterations, we find that the value of x converges to approximately 24.662174.
Therefore, the solution to the equation ln(x) = x - 31, correct to six decimal places, is x ≈ 24.662174.
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What is so soothing about the ocean? And why are some people afraid of the ocean?
Answer:
hydrophobiaExplanation:
it is phobia of waterand please add me on sñap
arshad2623fI hope u will add meThe ocean is very calm and beautiful its so soft and the waves are beautiful especially at night.
Some people are afraid of the ocean because of probably sharks, fish, or those grass in the ground. some times they think the ocean is going to take them away i think thats a phobia.
why is it important to have regular super vision of the weights and the measurements in the market?
Answer:
Obeying to weights & measurement regulations in both national and international metrology legislation, standards and test procedures is a requirement to participate in any market because it's aimed to safeguard the consumers and promote fair competition, which provides efficiency and saves unnecessary costs to U.S. businesses and stakeholders.
Explanation:
In the U.S., the National Institute of Standards and Technology (NIST) has an Office of Weights and Measures (OWM) that represents the country in the International Organization of Legal Metrology (OIML)
If it took 3 hours to clean 6 houses, how many houses could be cleaned in 12 hours?
Answer:
24
Explanation:
If it took 3 hours to clean 6 houses than you can figure that is 2 houses per hours. so if there are 12 hours and 2 houses an hour, you multiply 12x2 and get 24. Another way to do it is to use proportions (aka two fractions that equal eachother):
3 hours 12 hours
---------------- = ---------------
6 houses number of houses
To calculate this, we can think about how we go from 3 to 12. Well, 3x4 is 12, so we got to 12 by doing multiplying by 4. So we can multiply 6 by 4 and you get 24.
Hope it helps! have a great day :)
A train is traveling at 44 m/s as it approaches a station. If the train's normal acceleration is 2.2 m/s2 and it takes 27 s for the train to come to a complete stop, how far in front of the station should the engineer apply the brakes?
Answer:
s = 1989.9 m
Explanation:
In order to find the distance at which the engineer should apply brake, we can use 2nd equation of motion. The second equation of motion is as follows:
s = Vi t + (0.5)at²
where,
s = distance from the station = ?
Vi = Initial velocity = 44 m/s
t = time required to stop = 27 s
a = acceleration of train = 2.2 m/s²
Therefore,
s = (44 m/s)(27 s) + (0.5)(2.2 m/s²)(27 s)²
s = 1188 m + 801.9 m
s = 1989.9 m
Which combination of characteristics produces the LEAST energetic waves?
.
A. short wavelength, low frequency
B. short wavelength, high frequency
C. long wavelength, low frequency
D. long wavelength, high frequency
Answer:
C.
long wavelength, low frequency
Explanation:
The energy of wave depends on the wave frequency and wave amplitude.
The Wave energy can also be determined by wavelength, wave speed, amplitude, water density e.t.c
According to the question that
Which combination of characteristics produces the LEAST energetic waves ?
The correct option will be
C. long wavelength, low frequency
Option C is therefore the correct answer.
Answer:
Explanation:
c
What is a scientific law?
Answer:
In general, a scientific law is the description of an observed phenomenon. It doesn't explain why the phenomenon exists or what causes it. The explanation of a phenomenon is called a scientific theory. It is a misconception that theories turn into laws with enough research.
Explanation:
hope you get it right
:)
Answer: Found this in google. Statement based on repeated experiments or observations, that describe or predict a range of natural phenomena. Hope this helps!
Explanation:
How does a battery produce an electric current in a circuit ?
Answer:
A battery is a device that stores chemical energy and converts it to electrical energy. The chemical reactions in a battery involve the flow of electrons from one material to another, through an external circuit. The flow of electrons provides an electric current that can be used to do work.
A balloon has a volume of 1.80 liters at 24.0°C. The balloon is heated to 48.0°C. Calculate the new volume of the balloon. O a. 1.95 L Ob. 1.80 L O c. 1.67 L O d. 3.60 L Oe. 0.90 L >> Question 4 of 5 > Moving to another question will save this response.
The new volume of the balloon when heated to 48.0°C is approximately 1.95 L (option a).
To calculate the new volume of the balloon when it is heated, we can use the formula derived from Charles's Law, which states that for a given amount of gas at constant pressure, the volume is directly proportional to its temperature in Kelvin.
The formula is V1/T1 = V2/T2, where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature.
First, we need to convert the temperatures from Celsius to Kelvin:
T1 = 24.0°C + 273.15 = 297.15 K
T2 = 48.0°C + 273.15 = 321.15 K
Now, we can plug in the values into the formula:
V1 = 1.80 L (given)
T1 = 297.15 K
T2 = 321.15 K
1.80 L / 297.15 K = V2 / 321.15 K
Solving for V2, we get:
V2 = (1.80 L * 321.15 K) / 297.15 K
V2 ≈ 1.95 L
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5. A bullet accelerates at 5.8 x 10 m/s from rest as it travels the 0.80 m of the
rifle barrel.
a
How long was the bullet in the barrel?
b. What velocity does the bullet have as it leaves the barrel?
Answer:
Below
Explanation:
d = 1/2 a t^2
.80 = 1/2 ( 5.8 x 10^?) t^2
( I think you left off the exponent...and acceleration has units m/s^2 ...not m/s)
t = .166 s
v = at = 58 x .166= 9.63 m/s
The Sackur-Tetrode equation for the entropy of an ideal gas is given by (Blundell and Blundell ch 21): S = NkB [2 3 [2 - In (pX³h)], where p = N/V is the (number) density of the gas, and Ath = h/√2πmkBT is the thermal wavelength. a) [5 marks] Show that S is an extensive quantity. b) [5 marks] Show that the entropy of a gas of distinguishable particles is instead given by 3 S = NKB Nkw [-In ()] hint: use the relationship S = where F is the Helmholtz free energy. c) [5 marks] Show that the quantity in b) is not extensive
a. The Sackur-Tetrode equation has the entropy to be S = NkB [2 + 3[2 - ln(pX³h)]
b. 3S = NkB ln(V / Nλ³ shows the entropy of a gas with distinguishable particles
c. The quantity 3S = NkB ln(V / Nλ³) is not an extensive quantity because it does not scale linearly with the size of the system.
How do we calculate?a)
Entropy in the Sackur-Tetrode equation is denoted by S = NkB [2 + 3[2 - ln(pX3h)],
N = particle count,
kB = Boltzmann constant,
p = gas's number density,
X = thermal wavelength,
h = Planck's factor.
When we consider two systems, each with a different number of particles and volume, the entropy of the combined system is equal to the sum of the entropies of the individual systems.
b) The entropy is given by 3S = NkB ln(V / Nλ³),
where V = volume,
N= total number of particles,
λ= thermal wavelength.
The Helmholtz free energy (F) is defined as
F_ = U - TS.
IF we differentiate the Helmholtz free energy with respect to temperature (T), we can obtain the entropy expression 3S = NkB ln(V / Nλ³).
c)
Because it does not increase linearly with system size, the amount 3S = NkB ln(V / N3) is not a large quantity. In a large quantity, doubling the system's size would also double the quantity's value.
In this our scenario, doubling the system size would not result in a doubling of the entropy. As a result, it is not regarded as a large number.
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