The dU/dT at constant P and V is simply nR/P.
According to the ideal gas law, PV = nRT, so we can write P = nRT/V. Using this relationship, we can express the internal energy U as a function of P, V, and T:
U = f(P,V,T) = f(nRT/V, V, T)
To find dU/dP at constant V and T, we can use the chain rule:
dU/dP = (∂U/∂P)V,T + (∂U/∂V)P,T(dP/dP)V,T + (∂U/∂T)P,V(dT/dP)V,T
Since V and T are being held constant, we can simplify the second and third terms to just 0:
dU/dP = (∂U/∂P)V,T
To find (∂U/∂P)V,T, we can differentiate f(nRT/V, V, T) with respect to P, keeping V and T constant:
(∂U/∂P)V,T = (∂f/∂P)nRT/V(-nRT/V²) = -nRT/V²
So, dU/dP at constant V and T is simply -nRT/V².
To find dU/dT at constant P and V, we can again use the chain rule:
dU/dT = (∂U/∂T)P,V + (∂U/∂V)P,T(dV/dT)P,V + (∂U/∂P)V,T(dP/dT)P,V
Since P and V are being held constant, we can simplify the third term to just 0:
dU/dT = (∂U/∂T)P,V + (∂U/∂V)P,T(dV/dT)P,V
To find (∂U/∂T)P,V, we can differentiate f(nRT/V, V, T) with respect to T, keeping P and V constant:
(∂U/∂T)P,V = (∂f/∂T)nRT/V(1) = nR/V
To find (∂U/∂V)P,T, we can differentiate f(nRT/V, V, T) with respect to V, keeping P and T constant:
(∂U/∂V)P,T = (∂f/∂V)nRT/V(-nRT/V²) + (∂f/∂V)V,T = nRT/V² - nRT/V² = 0
Since the ideal gas law shows that PV = nRT, we can write V = nRT/P. Using this relationship, we can simplify the second term of dU/dT to just:
dU/dT = (∂U/∂T)P,V = nR/P
So, dU/dT at constant P and V is simply nR/P.
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a. To find dU/dPv, we need to differentiate U with respect to both P and V while treating T as a constant. Using the chain rule, we have:
dU/dPv = (∂U/∂P)v + (∂U/∂V)p * (dV/dP)v
Since U is a function of P, V, and T, we can express it as U(P,V,T). Using the ideal gas law, we substitute P = nRT/V into U:
U = f(P,V,T) = f(nRT/V, V, T)
Differentiating U with respect to P while treating V and T as constants, we get (∂U/∂P)v = -nRT/V².
Similarly, differentiating U with respect to V while treating P and T as constants, we get (∂U/∂V)p = nRT/V.
Hence, dU/dPv = -nRT/V² + nRT/V * (dV/dP)v.
b. To find dU/dTv, we differentiate U with respect to both T and V while treating P as a constant. Using the chain rule:
dU/dTv = (∂U/∂T)v + (∂U/∂V)t * (dV/dT)v
Differentiating U with respect to T while treating V and P as constants, we get (∂U/∂T)v = (∂f/∂T)v.
Similarly, differentiating U with respect to V while treating T and P as constants, we get (∂U/∂V)t = (∂f/∂V)t.
Hence, dU/dTv = (∂f/∂T)v + (∂f/∂V)t * (dV/dT)v.
Note: The specific form of the function f(P,V,T) is not provided, so we cannot determine the exact values of (∂f/∂T)v, (∂f/∂V)t, and (dV/dT)v without additional information.
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A wooden plank is 424cm long.
50% of it is cut off.
How long is the plank now?
Answer:
214cm long of wooden plank
what times what equals 168 besides 84 times 2?
Answer:
12 & 14
Step-by-step explanation:
A random sample of 1000 people who signed a card saying they intend to quit smoking were contacted 9 months later. Turned out that 210 (21%) of the sampled individuals had not smoked in the past 6 months. What is the population, parameter, sample and statistic?
Answer:
Population is the total number of people that fall into the description of those that the research concerns.
In this case, Population is: Everyone who signed a card saying that they intend to quit smoking.
Sample. This is a subset of the population that the research is based on.
Sample = 1,000 people surveyed.
Parameter and Statistic are both descriptive measures but parameter is for the population and statistic is for the sample.
Parameter = Percentage of total population who have not smoked in 6 months.
Statistic = 21% of sample who have not smoked in 3 months.
this from usatestprep
Answer:
either b or a
Step-by-step explanation:
Answer:
A I believe
Step-by-step explanation:
OFFERING BRAINLIEST !! Using the formula, compute the true annual interest rate to the nearest tenth.
[tex]Interest (I) = \frac{2yc}{m(n+1)}[/tex]
Loan amount = $9,500
Monthly payments = $227.50
Time of loan contract = 5 years
Interest rate = ____%
Answer:
Step-by-step explanation:
5x12=60
(227.5x5x120)=13650
13650-9500=4150
apply formula
(2x12x4150)/((13650(60+1))=0.1196
0.1196x100=11.96% 0r 12%
Answer:
17.2%
Step-by-step explanation:
given that:
y = 12 months
m = $9,500
n = 60 (because five years is 60 months)
c = (n * $227.50) - m
= (60 * $227.50) - $9,500
c = 4,150
and now, to substitute the following to the equation:
[tex]\frac{2(12)(4,150)}{9,500(61)} *100[/tex] = 17.2%
witch of the following statements are true
Write an expression that can be used to find the area of the shaded region.
Answer:
bkrjrjjrkrkrkririirkr
Find the total surface area
Answer:
47
Step-by-step explanation:
9+9+9+9+7+7
forgive me if i am wrong
Answer:
147 cm^2
Step-by-step explanation:
To find the surface area, you would have to add up the area of all shapes:
Area of triangle: 1/2 base*height
Area of square: length*width
----------
square = l*w = 7*7 = 49 cm^2
----------
So since there are 4 triangles, you would have to multiply the result by 4.
triangle = 1/2 7*9 = 49/2 = 24.5
4 triangles = area of 1 triangle * 4 = 4(24.5) = 98 cm^2
----------
add them up, and you get 49 + 98 = 147 cm^2
a, b ve c birbirinden farklı pozitif tam sayılardır.
Buna göre,
a.b.c = 12
eşitliğini sağlayan kaç değişik (a, b, c) üçlüsü vardır?
A) 6
B) 9
C) 12
D) 18
E) 24
A.6 would be the answer
A man walks 10 miles in x hours. How far does he walk in one hour?
Which expression represents this?
10 + x miles
10x miles
miles
Answer:
10/x represents how far he walks in one hour
Step-by-step explanation:
help need help ASAP
super hard? free brainly
Answer:
I think that is false, tell me if im wrong if you can
Answer:
Step-by-step explanation:
False I think.
WHAT VALUE ARE SOULTIONS TO X<7
Answer:
h M dan MB URL e5kei5
Step-by-step explanation:
h NBC qy2 il e5jrs
Please help please help please URGENT PLEASE NEED HELP PLEASE FAST RESPONSE PLEASE
Answer:
x = -4, x = 4
Step-by-step explanation:
A denominator cannot equal zero since division by zero is undefined.
Set the denominator equal to zero and solve for x. That will give you the values of x that would cause the denominator to be equal to zero and must be excluded from the domain.
x^2 - 16 = 0
(x + 4)(x - 4) = 0
x + 4 = 0 or x - 4 = 0
x = -4 or x = 4
Answer: x = -4, x = 4
The mid point of ab is m(-2,-6) if the coordinates of a are (-1,4) what are the coordinates of B
Answer:
i hate thsi coordinate chapter its very difficult chapter u know
What is m/3= -1.5 what is m???
Answer:
-4.5
Step-by-step explanation:
M would be -4.5 because if you multiply -1.5 by 3 you get -4.5. Therefore the equation would be -4.5/3= -1.5 .
Hope this helps :))
What is a venn diagram
Answer:
A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things
Venn diagrams help to visually represent the similarities and differences between two concepts.
50.0 divided by 100 equals??
Answer:
0.5
Step-by-step explanation:
Hopefully u got it right
Step-by-step explanation:
If you meant 50 divided by 100
[tex]\frac{50}{100} = \frac{1}{2}[/tex]
or just .5
If you meant 500 divided by 100
[tex]\frac{500}{100} = 5\\[/tex]
A pyramid has a rectangular base with edges of length 10 and 24. The vertex of the pyramid is directly 13 units above the center of the base. What is the: Total surface area of the pyramid?
Answer:
10 x 24 x 13 = 3120?
Step-by-step explanation:
I hope this is right!
Answer:
[tex]10\sqrt{313} +24\sqrt{194}+240[/tex] square units
Step-by-step explanation:
If your base is 10x24, and the vertical height is 13, you first have to find the slant height of the pyramid, in other words, calculate the hypotenuse of the triangles constructed using the height and the base divided by 2. You will need to find two slant heights as the base is not square. If you look at that image, the slant heights are marked in blue, and the specific measurements know are given in red. Using that, we can apply the Pythagorean theorem to determine the slant heights, which are [tex]\sqrt{194}[/tex] and [tex]\sqrt{313}[/tex], then we need to calculate the area of each triangular face. Thus they are [tex]5\sqrt{313}[/tex] and [tex]12\sqrt{194}[/tex], but there are two identical faces in the pyramid, which means we should double the area of the faces to achieve [tex]10\sqrt{313} +24\sqrt{194}[/tex], then we need to simply add the base as it's a face. So the answer is [tex]10\sqrt{313} +24\sqrt{194}+240[/tex]
if you could answer this that would be so appreciated :).
Given are the lengths of two sides of a triangle. Find the range of the lengths for the third side. this is triangle inequality theorem.
1. 3.6, 10.8
2. 6.9, 3.2
3. 6, 4
I’m sorry for spam but I really need help
Only answer is you know the answer plz!
Answer:Triangle Inequality Theorem
The Triangle Inequality theorem states that
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
The Converse of the Triangle Inequality theorem states that
It is not possible to construct a triangle from three line segments if any of them is longer than the sum of the other two.
The length of s is greater than 3 and less than 11
Step-by-step explanation:
Find the GCF 36, 22.
Answer:
The greatest common factor (GCF) of 36 and 22 is 2.
Answer:
2 is the GCF of 36 and 22.
the sum of three consecutive even numbers is 78,find the number
Answer:
24, 26, 28
Step-by-step explanation:
The final number is 78
first we can divide 78/3= 26
so 26+26+26= 78
we can leave the middle 26 but we can give 2 from the first number to the last number
24+26+28=78
(This might be wrong but i tried my best)
f(x)=x^3-6x^2+11x-6 is (x-4)
Answer: 10
Step-by-step explanation:
Answer:
x-4
Step-by-step explanation:
trust me!!
1.p + 8 = 14.1 *hgtyyytghg
Answer:
Let's solve your equation step-by-step.
p+8=14.1
Step 1: Subtract 8 from both sides.
p+8−8=14.1−8
p=6.1
Answer:p=6.1
help plz. thank u so much.
Answer:
i think x/y=4
Step-by-step explanation:
one and sixty three hundreths in decimal form.
Answer:
1.63
Step-by-step explanation:
Answer:
1.63
Step-by-step explanation:
which of the following is true about the expression
can someone please help? I'm sorry I don't have a lot of points to offer. I'm running out of points
Answer:
80 degrees
Step-by-step explanation:
The 132-deg angle is an exterior angle of the left triangle.
The 52-deg angle is a remote interior angle to the exterior angle above.
Angle VZY is also a remote interior angle to the exterior angle above.
Theorem:
The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.
We use the theorem above to find the measure of angle VZY.
52 + m<VZY = 132
m<VZY = 80
Angles WZX and VZY are vertical angles, so they are congruent.
m<WZX = m<VZY = 80
Answer: 80 degrees
Answer:
m∠WZX = 80°
Step-by-step explanation:
Angle V is a flat angle, so it measures 180°.
Find ∠YVZ (blue angle): 180° - 132° = 48°
Triangle VYZ is 180° (all triangles are 180°).
Find ∠YZV (red angle): 180° - 52° - 48° = 80°
Since you know ∠YZV, you can find ∠WZX (green angle).
∠YZV and ∠WZX are opposite angles, so they are congruent.
Therefore, ∠WZX = 80°
Hope this helps :)
H(x)=(x+5) ^2
If we solve h(x) = 36, one of the possible values of x is 1
What is the other possible value of x?
To solve this equation we must first -
2x - 4= 10
O subtract 4 from both sides
O add 4 to both sides
divide by 4
O multiply by 4
Answer:
divide by 4
Step-by-step explanation:
2x - 4 = 10
10 ÷ 4 = 2.5
2.5 ÷ 2 = 1.25
x = 1.25
Answer:
ADD 4 to both sides
Step-by-step explanation:
2x-4=10
2x+4=10+4
2x=10+4
2x=14
2x/14
x=7
Hope this helps:)
4x=-20 solve for x show your work
Answer: x = 5
Step-by-step explanation:
Answer:
x = -5
Step-by-step explanation:
We have the expression 4x = -20 and are asked to solve x.
To solve, we need to isolate x.
4x = -20
Divide 4 :
x = -5