The cylinder contains mw = 1.80 kg of water at just under 100°C. The piston has a radius of r = 6.35 cm, mass of mp = 2.70 kg, and initially rests on the surface of the water. The heater transfers energy to the water at the rate of 150 W. The latent heat of vaporization of water is Lvap = 2.26 ✕ 106 J/kg, and the specific heat of steam is csteam = 2,010 J/(kg ° C). The top of the piston is exposed to atmospheric pressure.
Answers
Here is the complete question.
The cylinder contains mw = 1.80 kg of water at just under 100°C. The piston has a radius of r = 6.35 cm, mass of mp = 2.70 kg, and initially rests on the surface of the water. The heater transfers energy to the water at the rate of 150 W. The latent heat of vaporization of water is Lvap = 2.26 ✕ 106 J/kg, and the specific heat of steam is csteam = 2,010 J/(kg ° C). The top of the piston is exposed to atmospheric pressure.
Once the water begins boiling, how fast does the piston rise ( in mm/s)?
Answer:
thus, once the water begins boiling, the speed of the piston rise is 8.73 mm/s
Step-by-step explanation:
Given that:
\(m_w =\) 1.80 kg
radius r = 6.35 cm
\(m_p =\) 2.70 kg
rate of energy transfer = 150 W
latent heat of vaporization of water \(L_{vap} = 2.26 * 10^6 J/kg\)
specific heat of steam is \(c_{steam} = 2,010 J/(kg ^0 C)\)
From the given information;
the speed rise of the piston can be perceived to be of the same rate at which the height of the steam above the water is also increasing due to boiling.
Thus; volume of the gas \(v = \dfrac{dh}{dt}\)
\(v = \dfrac{d}{dt}(\dfrac{V}{A})\)
Using the ideal gas law to replace the volume of the gas where the pressure and temperature are constant: we have;
\(v = \dfrac{1}{A} \dfrac{d}{dt}(\dfrac{nRT}{P})\)
\(v = \dfrac{RT \ \ dn}{PA \ \ dt}\)
However; the number of moles n in the mass \(m_g\) of the gas to the molecular mass \(M_w\) is ; \(n = \dfrac{m_g}{M_w}\)
Replacing that into the above velocity formulae; we have:
\(v = \dfrac{RT \ \ d}{(m_pg+ P_oA)}( \dfrac{m_g}{M_w})\)
where F = PA and F is the product of atmospheric pressure and area of piston plus the weight of the piston; i.e \(F = m_pg+ P_oA\)
\(v = \dfrac{RT \ \ d}{(m_pg+ P_oA)}( \dfrac{m_g}{M_w})\)
\(v =[\dfrac{RT }{(m_pg+ P_oA)M_w}]( \dfrac{dm_g}{dt})\)
where;
\(Q = \pm (\Delta mL)\)
\(\dfrac{dm_g}{dt}= \dfrac{d}{dt}( \dfrac{Q}{L_v})\)
Again;
\(v =[\dfrac{RT }{(m_pg+ P_oA)M_w}]( \dfrac{d}{dt})(\dfrac{Q}{L_v})\)
\(v =[\dfrac{RT }{(m_pg+ P_oA)M_w * L_v}]( \dfrac{dQ}{dt})\)
\(v =[\dfrac{RT \ \ Power}{(m_pg+ P_oA)M_w * L_v}]\)
\(v =[\dfrac{(8.314*373)(150)}{((2.70*9.8)+ (1.013*10^5)(\pi*0.0635^2))(0.0180 * 2.26*10^6}]\)
\(v = 8.73*10^{-3} \ m/s\\\)
\(v = 8.73 \ \ mm/s\\\)
Related Questions
x>-2
Wyatt wants to spend no more than $25 at the grocery store. He bought a
pizza for $7.55 and a cake for $11.02 (including tax). Choose the inequality
that he can use to find how much money he can still spend.
Answers
Answer:
he spent $18.57 and he can spend $7.43 more
The solution is, he can still spend no more than $6.43.
What is inequality?An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
here, we have,
given that,
Wyatt wants to spend no more than $25 at the grocery store.
He bought a pizza for $7.55 and a cake for $11.02 (including tax).
now, we have to find the inequality that he can use to find how much money he can still spend.
let, we would spend = x
now, we have,
He bought a pizza for $7.55 and a cake for $11.02
so, he had = $ x - ( 7.55 + 11.02)
we have,
x ≥ 25
so, he can still spend ≥ 25 - ( 7.55 + 11.02)
or, he can still spend ≥ 6.43
i.e. he can still spend no more than $6.43
Hence, The solution is, he can still spend no more than $6.43.
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perimeter 254 meters and dimension measures 6 meters
Answers
Answer:
didn't even ask a question
Step-by-step explanation:
impossible to answer without a question
Cuando hay una potencia de una potencia se conserva la base y los exponentes se multiplican? Verdadero o falso
Answers
Verdadero. Cuando hay una potencia de una potencia, se conserva la base y los exponentes se multiplican.
What is the statement about?Para calcular la potencia de una potencia, se puede conservar la base y multiplicar los exponentes. Esto se basa en la propiedad matemática de la potenciación que establece que (a^b)^c = a^(b*c), donde a es la base, b es el primer exponente y c es el segundo exponente.
Por ejemplo, considere (2³)⁴. La base es 2 y el primer exponente es 3 y el segundo exponente es 4. El resultado sería 2^(3*4) = 2¹². Esto significa que la expresión original (2³)⁴ es igual a 2 elevado a la potencia de 12.
En general, cuando se tiene una potencia de una potencia, el resultado se obtiene conservando la base y multiplicando los exponentes. Esto permite simplificar la expresión y encontrar el resultado de manera más fácil.
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if 104=10,000, which is equal to 4?; which equation is equivalent to a5=21?
Answers
If \(10^{4}\)= 10,000, then the value of 4 = \(log_{10}\) 10000. and the equation equivalent to \(a^{5}\) = 21 is 5 = \(log_{a}\) 21.
The logarithm is the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if \(b^{x}\) = n, which can be written as x = \(log_{b}\) n.
For example, \(2^4\) = 16; therefore, 4 is the logarithm of 8 to base 2, or 4 = \(log_{2}\) 8.
a. Here, 4 is the power of the 10, and we will express it in the log form. 4, is the logarithm of 10000 to base 10 or mathematically we can express it as -
4 = \(log_{10}\) 10000.
b. Similarly, we have to find the equation equivalent to \(a^{5}\) = 21
using the log form, we get that 5 is the logarithm of 21 to base a.
Mathematically we can express it as -
5 = \(log_{a}\) 21.
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The complete question is -
If \(10^{4}\) = 10,000, which is equal to 4? Which equation is equivalent to \(a^{5}\) = 21?
turn to improper fraction 4 1/7
Answers
Answer:
29/7
Explanation:
It just is
Sarah used 3 pound of blueberries to make 1 cup of jam. How many pounds of blueberries would she need
42
to make a cup of jam?
Answers
Answer:
126 pounds of blueberries
Step-by-step explanation:
1cup of jam=3pounds of blueberries
42cups of jam=?
42 X 3=126
Which graph shows a line with the slope of 3/2
Answers
Also, can you mark my answer as the brainliest answer?
Thanks
Mr Tan bought a house for $410 000. He paid a deposit of 30% and took on a loan for the remaining amount. How much was his loan? Give your answer
correct to the nearest ten thousands.
Answers
Answer:
The amount of the loan Mr. Tan borrowed was $ 287,000.
Step-by-step explanation:
Since Mr. Tan bought a house for $ 410,000, paying a deposit of 30% of its value and requesting a loan for the rest of its value, to determine the amount of the loan, the following calculation is required:
100 - 30 = 70
410,000 x 0.70 = X
287,000 = X
Therefore, the amount of the loan Mr. Tan borrowed was $ 287,000.
Adventure Travel has an Adjusted Trial Balance for Year Ended December 31, 20XX with the following account balances:
DEBITS: Cash: 25,000; Accounts Receivable: 15,000; Office Supplies: 4,300; Office Equipment: 29,600
CREDITS: Accumulated depreciation - office equipment: 5,000; Salaries Payable: 2,800; Long-term notes payable: 22,200; Common Stock: 20,000; Retained Earnings: 10,260
DEBIT: Cash Dividends: 1,000
CREDITS: Fees Earned: 75,000
DEBITS: Salaries Expense: 32,800; Rent Expense: 16,800; Depreciation expense - office equipment: 3,960; Advertising expense: 4,000; Office supplies expense: 2,800.
Total Debits = 135,260; Total Credits = 135,260
You have just determined Net Income for Adventure Travel in the previous question. Now, you must prepare the Statement of Retained Earnings.
What is the Retained Earnings Balance as of the Ending of the Year, December 31, 20XX? Specify whole number.
Answers
The Retained Earnings Balance as of the Ending of the Year, December 31, 20XX is $23,900
What is net income?
The net income is the excess of fees earned by Adventure Travel in the year ended over its total expenses, in essence, we need to determine its total expenses first and foremost, which comprises of salaries expense, rent expense, depreciation expense, advertising expense and office supplies expense
total expenses=32,800+16,800+3960+4000+2800
total expenses=60,360
fees earned=75,000
net income =fees earned-total expenses
net income=75,000-60,360
net income=$14,640
Now the closing retained earnings comprises of beginning retained earnings plus the net income minus the cash dividends paid
Retained earnings=$14,640+$ 10,260-$1,000
Retained earnings=$23,900
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i really need help!!!!!
there are like 5 questions.
Answers
Answer:
3
Step-by-step explanation:
The answer is three because u need to simply the fractions
Hi, which one is the correct answer? thank you
Answers
Answer:
Step-by-step explanation:
tan B=372/279=(31×12)/(31×9)=12/9=4/3
Please please help
I haven’t had WiFi and I have over 18 days of This
Answers
Answer:
Step-by-step explanation: a= E
b=D
c=A
Answer:
A. E
B. D
C. A
Step-by-step explanation:
A tank contains 2840 L of pure water. A solution that contains 0.07 kg of sugar per liter enters a tank at the rate 4 L/min The solution is mixed and drains from the tank at the same rate. (a) How much sugar is in the tank initially? A(0)= 0 (kg) (b) State the rate at which the sugar is entering the tank. (kg/min) (c) State the concentration of sugar in the tank at time t, using the letter A to represent the amount of sugar in the tank at time t. (kg/L) (d) State the rate at which the sugar is leaving the tank, Rout, using the letter A to represent the amount of sugar in the tank at time t. (kg/min) (e) State the differential equation representing the rate at which the amount of sugar in the tank is changing at time t.
Answers
Answer:
(a) A(0)= 0 (kg)
(b) \(R_{in}=0.28\dfrac{kg}{min}\)
(c) \(C(t)=\dfrac{A(t)}{2840}\)
(d) \(R_{out}=\dfrac{A(t)}{710}\)
(e) \(\dfrac{dA}{dt}=0.28-\dfrac{A(t)}{710}\)
Step-by-step explanation:
A tank contains 2840L of pure water.
A solution that contains 0.07 kg of sugar per liter enters a tank at the rate 4 L/min. The solution is mixed and drains from the tank at the same rate.
(a) Amount of sugar initially in the tank.
Since the tank initially contains pure water, the amount of sugar in the tank
A(0)= 0 (kg)
(b) Rate at which the sugar is entering the tank. (kg/min)
\(R_{in}\)=(concentration of sugar in inflow)(input rate of the solution)
\(=(0.07\dfrac{kg}{liter}) (4\dfrac{liter}{min})\\R_{in}=0.28\dfrac{kg}{min}\)
(c) Concentration of sugar in the tank at time t
Volume of the tank =2840 Liter
Concentration c(t) of the sugar in the tank at time t
Concentration, C(t)= \(\dfrac{Amount}{Volume}\)
\(C(t)=\dfrac{A(t)}{2840}\)
(d) Rate at which the sugar is leaving the tank
\(R_{out}\)=(concentration of sugar in outflow)(output rate of solution)
\(=\dfrac{A(t)}{2840})( 4\dfrac{Liter}{min})=\dfrac{A}{710}\\R_{out}=\dfrac{A(t)}{710}\)
(e) Differential equation representing the rate at which the amount of sugar in the tank is changing at time t.
\(\dfrac{dA}{dt}=R_{in}-R_{out}\\\dfrac{dA}{dt}=0.28-\dfrac{A(t)}{710}\)
8. In the 24-hour clock system, midnight is written as ____.
Answers
In the 24-hour clock system, midnight is written as _0h_
Answer:
00:00
Step-by-step explanation:
A cylindrical bucket contains 615 cubic inches of water the heigh of the water is 4 inches what is the radius of the bucket to the nearest whole number
Answers
Answer:
Your answer is: 5 or 6 inches
Step-by-step explanation:
Hope this helped : )
0 8. A function f(x) is said to have the jump discontinuity at a point x = a if lim a)x+a+ c) x→a+ f(x) = lim x→a+ f(x) = lim x→a¯ lim X-a f(x). b) lim x→a f(x) = lim x→a¯ _ f(x) f(x) = f(a) d) lim f(x) → +00 x→a+
Answers
The correct option for the given question is c) lim x→a¯ f(x) = f(a) when the function f(x) is said to have jump discontinuity at a point x=a.
What is jump discontinuity?Jump continuity is a concept in calculus that describes the behaviour of a function at a specific point where the function jumps from one value to another value without any intermediate values. In other words, a function is considered jump continuous at a point if the function approaches a finite limit from both the left and right sides of that point, but the function values on the left and right sides of the point are not equal.
According to the given information:
The correct notation for the left-hand limit as x approaches a from the left side is lim x→a¯, where the horizontal line above the "a" indicates approaching from the left side.
The statement "lim x→a¯ f(x) = f(a)" means that the limit of f(x) as x approaches a from the left side is equal to the value of f(a) at x = a. This indicates that the function f(x) has a jump discontinuity at x = a, where the function jumps from one value to another value at that specific point.
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Have a screenshot of math question, check pick below plz thanks
Answers
Answer:
i dont see it
Step-by-step explanation:
What should I choose
Answers
Answer:
5x+18y
Step-by-step explanation:
3x+2x=5x
11y+7y=18y
Combine Like terms
3x + 2x = 5x
11y - 7y = 4y (I'm asumming that the blanks are subtracting signs)
Therefore, 5x + 4y
7 1/2 divided by 1/4
Answers
Answer: 30
Step-by-step explanation:
Answer:
Its 30
Step-by-step explanation:
multiply the 7 with its denominator, 2. Then add that result to the numerator, 1. You should get 15/2. Change the division sign to the multiplication sign. While you do that, flip 1/4 to 4/1. Multiply 15/2 and 4/1. Simplify the 4 and 2 which they can be to 2 and 1. Then there should be nothing below 15, just itself as a whole number and 2 it self with nothing below it either. Multiply 15 and 2 and there’s your answer!! 30!! Woohoo!!
Steven earns extra money babysitting. He charges $25.00 for 4 hours and $43.75 for 7 hours.
Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits and y represent the amount he charges.
Answers
Answer:
An easy way to solve this problem is divide $25.00 by 3 or $43.75 by 7. This number represents the amount of money he makes for 1 hour. So with that in mind, the correct equation is:
$8.33 = y
Hope this helped :)!
Help pls PLS HELP HELP
Answers
160 = (3x + 10)
160 - 10 = 3x
150 = 3x
150/3 = x
X = 50
Which describes the slope of a vertical line? O zero e positive O undefined e negative
Answers
When the slope of a line is very high, the line approaches to be a vertical line.
So when we have a line that approaches a vertical line, its slope approaches infinity.
Therefore the slope of a vertical line is undefined.
(Opposite to that, the slope of a horizontal line is zero)
A bakery wanted to make their muffins more uniform in size. They reworked their equipment to do so. To test the changes, they made 25 muffins then measured each one. Which of the following should they use to determine whether or not the equipment changes worked?
Select one:
a.
mean
b.
mode
c.
range
d.
interquartile range
Answers
Jose swims 3 laps in a pool every 2 minutes. How long would it take him to swim 27 laps? Group of answer choices 8 minutes 9 minutes 16 minutes 18 minutes
Answers
Answer:
18 minutes
Step-by-step explanation:
\(3\:laps = 2\:minute\\27\:laps = x\:minute\\\\Cross\:Multiply\\3x = 54\\\\Divide\:both\:sides\:of\:the\:equation\:by\:3\\\frac{3x}{3}= \frac{54}{3} \\\\x = 18\:minutes\)
Answer:
x =18
Step-by-step explanation:
We can use ratios to solve
3 laps 27 laps
----------- = ---------------
2 minutes x minutes
Using cross products
3x = 2 * 27
3x = 54
Divide by 3
3x/3 = 54/3
x =18
An artist is creating a large butterfly sculpture outside a museum. There is a circular dot on each wing made out of a metal ring. The distance around each dot is 24 inches
The artist plans to fill the inside of each dot with blue colored glass.
What is the area of the blue glass will be needed to fill each butterfly dot?
Give your answer in terms of pi.
Answers
The area of this blue glass is equal to 144π square inches.
How to calculate the area of this blue glass?In order to calculate the area of this blue glass, we would have to first determine its radius by using the formula for the circumference of a circle. Mathematically, the circumference of a circle can be calculated by using this formula:
C = 2πr
Where:
C represents the circumference of a circle.r represents the radius of a circle.Next, we would determine the radius of this blue glass as follows:
Radius, r = C/2π
Substituting the given parameters into the formula, we have;
Radius, r = 24π/2π
Radius, r = 12 meters.
Mathematically, the area of a circle can be calculated by using this formula:
Area of a circle = πr²
Area of a circle = π × 12²
Area of a circle = π × 144
Area of a circle = 144π square inches.
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Complete Question:
An artist is creating a large butterfly sculpture outside a museum. There is a circular dot on each wing made out of a metal ring. The distance around each dot is 24pi inches. The artist plans to fill the inside of each dot with blue colored glass.
What is the area of the blue glass will be needed to fill each butterfly dot?
Give your answer in terms of pi.
Nancy believes that the average running time of movies is equal to 140 minutes. A sample of 4 movies was taken and the following running times were obtained. Assume the distribution of the population is normally distributed. 150 150 180 170
a. State the null and alternative hypotheses.
b. Using a critical value, test the hypothesis at the 10% level of significance.
c. Using a p-value, test the hypothesis at the 10% level of significance.
d. Using a confidence interval, test the hypothesis at the 10% level of significance.
e. Could a Type II error have been committed in this hypothesis test?
Answers
Answer:
a; H0: u= 140 Ha: u ≠ 140 two tailed test.
b. Therefore reject H0 as t= 3 ≠ t≤ t ( ∝/2) (n-1) =2.353 or
3 > t ( ∝/2) (n-1) =2.353
c. If we check from the table the p- value is 0.6 which lies between 0.1 and 0.05 therefore reject H0.
d. Again reject H0 as 140 < 150.163
e. A type II error has not been committed as H0 is rejected.
Step-by-step explanation:
We formulate the null and alternative hypotheses as
a; H0: u= 140 Ha: u ≠ 140 two tailed test.
For a two tailed test the significance level ∝= 0.1 the critical region is given by
t ≤ t ( ∝/2) (n-1) and t > t ( ∝/2) (n-1)
So the critical region will be
t≤ t ( ∝/2) (n-1) =2.353
where
t= x` - u / s/ √n
Sr. No X X²
1 150 22500
2 150 22500
3 180 32400
4 170 28900
∑ 650 106,300
X`= ∑x/n = 650/4= 162.5
s²= 1/n-1 (x-x`)²= 1/n-1 [ ∑x² -(∑x)²/n ]
= 1/3[106,300 -650²/4] = 225
s= 15
Putting the values in the above equation
t= 162.5- 140/ 15/ √4
t= 3
So calculated value of t= 3
b. Therefore reject H0 as t= 3 ≠ t≤ t ( ∝/2) (n-1) =2.353 or
3 > t ( ∝/2) (n-1) =2.353
c. If we check from the table the p- value is 0.6 which lies between 0.1 and 0.05 therefore reject H0.
d. a 90% confidence interval based on the calculated values will be
x`± 1.645 (s)/ √n
Putting the values
162.5 ±1.645 ( 15/2)
162.5 ±12.3375
174.84 , 150.163
d. Again reject H0 as 140 < 150.163
e. A type II error has not been committed as H0 is rejected.
Answer here:Assume the triangular prism has a base area of 36 cm² and a volume of 432 cm³. What base side length does the rectangular prism need to have the same volume?
Answers
Answer:
18 cm
Step-by-step:
The formula for the volume of a triangular prism is given by:
V_triangular_prism = (1/2) * base * height * length
where the base is the area of the base triangle, height is the perpendicular distance between the two parallel base planes, and length is the distance between the two triangular faces.
We are given that the base area of the triangular prism is 36 cm² and the volume is 432 cm³. Using these values, we can solve for the height:
432 = (1/2) * 36 * height * length
height * length = 24
Since we want to find the base side length of a rectangular prism that has the same volume, we can use the formula for the volume of a rectangular prism:
V_rectangular_prism = length * width * height
We know that the volume of the rectangular prism is also 432 cm³, so we can substitute this value and the value we found for the height * length product:
432 = length * width * height
432 = length * width * (24/length)
432 = 24 * width
width = 18
Therefore, the base side length of the rectangular prism needs to be 18 cm.
Hope this helps!
8.88=4.44(x+7) answer pls I need it asap!!!
Answers
To solve for x in the equation 8.88 = 4.44(x+7), we need to isolate x on one side of the equation. Here are the steps:
Distribute the 4.44 on the right side of the equation:
8.88 = 4.44x + 31.08
Subtract 31.08 from both sides of the equation:
-22.2 = 4.44x
Divide both sides by 4.44:
x = -5
Therefore, the solution for x in the equation 8.88 = 4.44(x+7) is x = -5.
To save for retirement, starting from her 30th birthday (t = 0), Miss Saver will invest
some money each year in a 30-year deposit in her bank saving account. The first
payment of $1000 will be made at the beginning of the first year. Every subsequent
payment increases by 5%.
She will retire at age 60, and will withdraw $X each year from her bank saving account
from then. The first withdrawal will be made at age 60. After 20 years (i.e. after the
20th withdrawal), she will have taken out all the money she had saved.
Assuming the effective annual interest rate is 2% perpetually, compute the value of X.
Give your answer to the nearest integer.
Answers
Miss Saver needs to withdraw $391 each year from her bank.
How to determine the value of XTo solve this problem, we need to
calculate the future value of the savings account at age 60,Then determine the annual withdrawal amount that will exhaust the account after 20 years.First, we need to determine the total amount of money Miss Saver will have saved using:
Total = $1000 * (1 + 0.05)^30 = 4321.94
Next, we need to determine the future value of this amount after 30 years at an effective annual interest rate of 2%.
This is done using
$4321.94 * (1 + 0.02)^30 = $7828.60
Now, we can determine the annual withdrawal amount, X as follows
X = $7828.59/20 = $391.4295
Rounding up to the nearest integer, X = $391
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Diven {x) = 3x- 1 and 9(x) = 2x-3, for which value of x does g(X) = {2)?
Answers
The calculated value of x at g(x) = 2 is x = 2.5
How to determine the value of x at g(x) = 2from the question, we have the following parameters that can be used in our computation:
f(x) = 3x - 1
Also, we have
g(x) = 2x - 3
When g(x) - 2, we have
2x - 3 = 2
So, we have
2x = 5
Divide by 2
x = 2.5
Hence, the value of x at g(x) = 2 is x = 2.5
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