One way to achieve this is by using an Apex Class to aggregate the amounts from the custom object. You could use a SOQL query to retrieve the data from the custom object, then loop through the records to calculate the rolling up amount. This can then be stored in a variable or set as a field on the Opportunity.
Using Apex Classes to Calculate Rolling Up Amounts from Custom ObjectsAchieving a rollup amount from a custom object that is not in a master-detail relationship can be a challenge. Fortunately, with the help of Apex Classes, this task can be achieved with relative ease. Apex Classes are powerful tools that allow developers to execute complex tasks within Salesforce, such as querying and manipulating data. In this case, an Apex Class can be used to query the custom object and loop through the records to calculate the rolling up amount. This amount can then be stored in a variable or set as a field on the Opportunity.
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Two sites are being considered for wind power generation. On the first site, the wind blows steadily at 7 m/s for 3000 hours per year. On the second site, the wind blows steadily at 10 m/s for 2000 hours per year. The density of air on the both sites is 1.25 kg/m3 . Assuming the wind power generation is negligible during other times.Calculate the maximum power of wind on each site per unit area, in kW/m2 .
Solution :
Given :
[tex]$V_1 = 7 \ m/s$[/tex]
Operation time, [tex]$T_1$[/tex] = 3000 hours per year
[tex]$V_2 = 10 \ m/s$[/tex]
Operation time, [tex]$T_2$[/tex] = 2000 hours per year
The density, ρ = [tex]$1.25 \ kg/m^3$[/tex]
The wind blows steadily. So, the K.E. = [tex]$(0.5 \dot{m} V^2)$[/tex]
[tex]$= \dot{m} \times 0.5 V^2$[/tex]
The power generation is the time rate of the kinetic energy which can be calculated as follows:
Power = [tex]$\Delta \ \dot{K.E.} = \dot{m} \frac{V^2}{2}$[/tex]
Regarding that [tex]$\dot m \propto V$[/tex]. Then,
Power [tex]$ \propto V^3$[/tex] → Power = constant x [tex]$V^3$[/tex]
Since, [tex]$\rho_a$[/tex] is constant for both the sites and the area is the same as same winf turbine is used.
For the first site,
Power, [tex]$P_1= \text{const.} \times V_1^3$[/tex]
[tex]$P_1 = \text{const.} \times 343 \ W$[/tex]
For the second site,
Power, [tex]$P_2 = \text{const.} \times V_2^3 \ W$[/tex]
[tex]$P_2 = \text{const.} \times 1000 \ W$[/tex]
During a shrinkage limit test, a 19.3 cm3 saturated clay sample with a mass of 37 g was placed in a porcelain dish and dried in the oven. The oven-dried sample had a mass of 28 g with a final volume of 16 cm3 . Determine the shrinkage limit and the shrinkage ratio.
Answer:
shrinkae limit = 20.35%
shrinkage ratio = 1.45
Explanation:
1. to get the shrinkage limit we would first calculate the moisture content w.
w = (37-28)/28
= 9/28
= 0.3214
then the formula for shrinkage limit is
[tex][w-\frac{(V-Vd}{wd} ]*100[/tex]
w = 0.3214
V = 19.3
Vd = 16
Wd = 28
when we put these values into the formula:
[tex][0.3214-\frac{(19.3-16)}{28} ]*100\\[/tex]
= 20.35%
2. the shrinkage limit = Wd/V
= 28/19.3
= 1.45
Where does Burj Khalifa located? and how many meters?
Answer:
Burj Khalifa is located in dubai UAE at over 828m
Explanation:
828 metres
Answer:
The Burji Khalifa, known as the Burj Dubai prior to its inauguration in 2010, is a skyscraper in Dubai, United Arab Emirates. With a total hight of 829.8 m and a roof hight of 828 m, the Burji Khalifa has been the tallest structure and building in the world since its topping out in 2009.
a load of 12tonnes is put along a horizontal plane by a force at 30°to and above the flat. if the coefficient of sliding friction is 0.2 find the frictional force
Answer:
20368.917N
Explanation:
Frictional force (F) is the product of the Coefficient of friction and the normal reaction.
F = μN
Coefficient of friction, μ = 0.2
Normal reaction = MgCosθ
Mass, m = 12 tonnes = 12 * 1000 = 12000 kg
N = 12000 * 9.8 * cos30
N = 101844.58
F = 0.2 * 101844.58
F = 20368.917N
A sign structure on the NJ Turnpike is to be designed to resist a wind force that produces a moment of 25 k-ft in one direction. The axial load is 30 kips. Soil conditions consist of a normally consolidated clay layer with following properties; su=800 psf, andγsat= 110 pcf. Design for a FOS of 3. Assume frost depth to be 3ft below grade
Solution :
Finding the cohesion of the soil(c) using the relation:
[tex]$c = \frac{q_u}{2}$[/tex]
Here, [tex]$q_u$[/tex] is the unconfined compression strength of the soil;
[tex]$c = \frac{800}{2}$[/tex]
= 400 psf
∴ The cohesion value is greater than 0
So the use of the angle of internal friction is 0
Referring to the table relation between bearing capacity factors and angle of internal friction.
For the angle of inter friction [tex]$0^\circ$[/tex]
[tex]$N_c = 5.14$[/tex]
[tex]$N_q = 1.0$[/tex]
[tex]$N_r = 0$[/tex]
Therefore,
[tex]$q_{ult} = (400 \times 5.14 )+(110 \times 3 \times 1.0)+(0.5 \times 100 \times 13 \times 0)$[/tex]
= 2386 psf
∴ Allowable bearing capacity [tex]$q_{a} = \frac{Q_{allow}}{A}$[/tex]
[tex]$=\frac{30}{B^2}$[/tex]
∴ [tex]$q_a = \frac{q_{ult}}{F.O.S}$[/tex]
[tex]$\frac{30}{B^2} = \frac{2386}{3}$[/tex]
∴ B = 0.2 ft
Therefore, the dimension of the square footing is 0.2 ft x 0.2 ft
[tex]$=0.04 \ ft^2$[/tex]
Experiment with a simple derivation relationship between two classes. Put println statements in constructors of both the parent and child classes. Do not explicitly call the constructor of the parent in the child classes. Do not explicitly call the constructor of teh parent in the child. What happens? Why? Change the child's constructor to explicitly call the constructor of the parent. Now what happens?
I need an example program in java, because I can't visualize what I am supposed to do, and I do need help with that, if you could send me the sample programs I would be grateful thank you.
In Java, when a class is derived from another class, a relationship is formed between them. This relationship is known as the inheritance relationship, where the derived class inherits properties and methods from the parent class.
When you create a new object of the child class, the constructor of the parent class is automatically called before the constructor of the child class is executed. This is because the child class needs to initialize all the properties that it inherited from the parent class.
Now, if you experiment with a simple derivation relationship between two classes and put println statements in constructors of both the parent and child classes, but do not explicitly call the constructor of the parent in the child classes, you will see that the parent class constructor is still called before the child class constructor. This is because it is done implicitly by Java.
Here is a sample program that demonstrates this:
```
class Parent {
public Parent() {
System.out.println("Parent constructor called");
}
}
class Child extends Parent {
public Child() {
System.out.println("Child constructor called");
}
}
public class Main {
public static void main(String[] args) {
Child childObj = new Child();
}
}
```
If you run this program, you will see the output as:
```
Parent constructor called
Child constructor called
```
Now, if you change the child's constructor to explicitly call the constructor of the parent, you will see that the output remains the same. However, the parent constructor is called explicitly this time.
Here is the modified sample program:
```
class Parent {
public Parent() {
System.out.println("Parent constructor called");
}
}
class Child extends Parent {
public Child() {
super();
System.out.println("Child constructor called");
}
}
public class Main {
public static void main(String[] args) {
Child childObj = new Child();
}
}
```
If you run this program, you will still see the output as:
```
Parent constructor called
Child constructor called
```
But this time, the parent constructor is called explicitly using the `super()` keyword inside the child's constructor.
I hope this helps you understand the inheritance relationship and how constructors work in Java. Let me know if you have any more questions.
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the "Parent" constructor was specifically called from the "Child" constructor. This is such that each constructor can either call a constructor in the superclass (called "super()") or a constructor in the same class (called "this()").
```
class Parent {
public Parent() {
System.out.println("Parent constructor called");
}
}
class Child extends Parent {
public Child() {
System.out.println("Child constructor called");
}
}
public class Main {
public static void main(String[] args) {
Child c = new Child();
}
}
```
In this program, we have two classes: `Parent` and `Child`. `Child` is a subclass of `Parent`, meaning it inherits all of `Parent`'s methods and fields.
In the `Parent` constructor, we simply print a message saying that the constructor was called. Similarly, in the `Child` constructor, we also print a message saying that the constructor was called.
In the `Main` class, we create an instance of `Child` by calling its constructor. Notice that we do not explicitly call the `Parent` constructor in the `Child` constructor.
If you run this program, you'll see the following output:
```
Parent constructor called
Child constructor called
```
This is because when we create a new `Child` object, the `Child` constructor is called first. Since the `Child` constructor does not explicitly call the `Parent` constructor, the `Parent` constructor is automatically called for us.
Now, let's change the `Child` constructor to explicitly call the `Parent` constructor:
```
class Child extends Parent {
public Child() {
super();
System. out.println("Child constructor called");
}
}
```
Notice that we added the `super()` statement, which calls the `Parent` constructor.
If you run this program now, you'll see the following output:
```
Parent constructor called
Child constructor called
```
The output is the same as before. However, this time, we explicitly called the `Parent` constructor in the `Child` constructor. This is because every constructor must call either another constructor in the same class (`this()`) or a constructor in the superclass (`super()`).
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Select the correct answer.
Alan is walking on a street and passes by a very busy construction site. He sees engineers hanging one end of various objects to the ceiling and the other end to heavy
weights. They observe the objects and then then take down notes. What are the engineers doing
Answer: the engineers are performing a tensile test
Explanation:
i took the test and got it right
A single crystal of a metal that has the FCC crystal structure is oriented such that a tensile stress is applied parallel to the [100] direction. If the critical resolved shear stress for this material is 2.00 MPa, calculate the magnitude of applied stress necessary to cause slip to occur on the (111) plane in the direction.
Answer:
Explanation:
From the given information:
The equation for applied stress can be expressed as:
[tex]\sigma_{app} = \dfrac{\tau_{CRSS}}{cos \phi \ cos \lambda}[/tex]
where;
[tex]\phi[/tex] = angle between the applied stress [100] and [111]
To determine the [tex]\phi[/tex] and [tex]\lambda[/tex] for the system
Using the equation:
[tex]\phi= cos^{-1}\Big [\dfrac{l_1l_2+m_1m_2+n_1n_2}{\sqrt{(l_1^2+m_1^2+n_1^2)(l_2^2+m_2^2+n_2^2)}}\Big][/tex]
for [100]
[tex]l_1 = 1, m_1 = 0, n_1 = 0[/tex]
for [111]
[tex]l_1 = 1 , m_1 = 1, n_1 = 1[/tex]
Thus;
[tex]\phi= cos^{-1}\Big [\dfrac{1*1+0*1+0*1}{\sqrt{(1^2+0^2+0^2)(1^2+1^2+1^2)}}\Big][/tex]
[tex]\phi= cos^{-1}\Big [\dfrac{1}{\sqrt{(3)}}\Big][/tex]
[tex]\phi= 54.74^0[/tex]
To determine [tex]\lambda[/tex] for [tex][1 \overline 1 0][/tex]
where;
for [100]
[tex]l_1 = 1, m_1 = 0, n_1 = 0[/tex]
for [tex][1 \overline 1 0][/tex]
[tex]l_1 = 1 , m_1 = -1, n_1 = 0[/tex]
Thus;
[tex]\lambda= cos^{-1}\Big [\dfrac{1*1+0*1+0*0}{\sqrt{(1^2+0^2+0^2)(1^2+(-1)^2+0^2)}}\Big][/tex]
[tex]\phi= cos^{-1}\Big [\dfrac{1}{\sqrt{(2)}}\Big][/tex]
[tex]\phi= 45^0[/tex]
Thus, the magnitude of the applied stress can be computed as:
[tex]\sigma_{app} = \dfrac{\tau_{CRSS}}{cos \phi \ cos \lambda }[/tex]
[tex]\sigma_{app} = \dfrac{2.00}{cos (54.74) \ cos (45) }[/tex]
[tex]\mathbf{\sigma_{app} =4.89 \ MPa}[/tex]
Which gas is released in the SMAW process causing a
shielding affect on the molten weld pool?
•nitrogen
•carbon dioxide
•argon
•hydrogen
If the hypotenuse of a right triangle is 12 and an acute angle is 37 degrees find leg a and leg b lengths
scrity añao devid codicie
Travel Time Problem: Compute the time of concentration using the Velocity, Sheet Flow Method for Non-Mountainous Orange County and SCS method at a 25 year storm evert.
Location Slope (%) Length (ft) Land Use
1 4.5 1000 Forest light underbrush with herbaceous fair cover.
2 2.5 750 Alluvial Fans (eg. Natural desert landscaping)
3 1.5 500 Open Space with short grasses and good cover
4 0.5 250 Paved Areas (1/4 acre urban lots)
Answer:
Total time taken = 0.769 hour
Explanation:
using the velocity method
for sheet flow ;
Tt = [tex]\frac{0.007(nl)^{0.8} }{(Pl)^{5}s^{0.4} }[/tex]
Tt = travel time
n = manning CaH
Pl = 25years
L = how length ( ft )
s = slope
For Location ( 1 )
s = 0.045
L = 1000 ft
n = 0.06 ( from manning's coefficient table )
Tt1 = 0.128 hour
For Location ( 2 )
s = 2.5 %
L= 750
n = 0.13
Tt2 = 0.239 hour
For Location ( 3 )
s = 1.5%
L = 500 ft
n = 0.15
Tt3 = 0.237 hour
For Location (4)
s = 0.5 %
L = 250 ft
n = 0.011
Tt4 = 0.165 hour
hence the Total time taken = Tt1 + Tt2 + Tt3 + Tt4
= 0.128 + 0.239 + 0.237 + 0.165 = 0.769 hour
Convert an acceleration of 12m/s² to km/h²
I don’t know the answer to this question
Answer:
I dont know the answer either
Explanation:
Answer:
flux
Explanation:
Which option identifies what is missing in the categorical syllogistic argument below? Quadrupeds have four legs so horses are quadrupeds.
Conclusion
Minor premise
Inference
Major premise
The three sub regions of South America are the Andes Mountains, the Amazon Rainforest, and the Eastern Highlands. The Atacama Desert is the driest place on Earth.
Answer:
<:
Explanation:
Answer:
d
Explanation:
Branch circuits shall be __________ in accordance with the maximum permitted.
210. 3
Branch circuits shall be sized in accordance with the maximum permitted.
What is the sizing requirement for branch circuits?The sizing of branch circuits ensure that they can safely and effectively carry the electrical load that will be placed on them. The National Electrical Code specifies the maximum ampacit or current-carrying capacity of branch circuits based on the size and type of wire being used.
So, it important to size branch circuits correctly to avoid overloading the circuit which can result in overheating, fires, and other hazards. The contractors and other professionals responsible for installing and maintaining electrical systems should be familiar with the NEC requirements for branch circuit sizing and ensure that all installations comply with these standards.
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The movement of the piston and connecting rod assembly driven by the force of combustion turns the ________.
Answer:
the answer. for this is Crankshaft
Suppose you are choosing between four different desktop computers: one is an Apple Mac Intosh and the other three are PC-compatible computers that use a Pentium 4, an AMD processor (using the same compiler as the Pentium 4), and a Pentium 5 (which does not yet exist in 2004 but has the same architecture as the Pentium 4 and uses the same compiler). Which of the following statements are true?
a. The fastest computer will be the one with the highest clock rate.
b. Since all PCs use the same Intel-compatible instruction set and execute the same number of instructions for a program, the fastest PC will be the one with the highest clock rate.
c. Since AMD uses different techniques than Intel to execute instructions,they may have different CPIs. But, you can still tell which of the two Pentium-based PCs is fastest by looking at the clock rate.
d. Only by looking at the results of benchmarks for tasks similar to your workload can you get an accurate picture of likely performance.
Answer:
d.
Explanation:
1. What is the productivity rate using cycle time for the following information:
I
Type of Work – Hauling
Average Cycle Time – 35 Minutes
Truck Capacity – 25 Tons
Crew - One Driver
Productivity Factor - 0.85
System Efficiency – 55 Minutes
per
Hour
Now, you get a turn to practice writing a short program in Scratch. Try to re-create the program that was shown that turns the sprite in a circle. After you have completed that activity, see if you can make one of the improvements suggested. For example, you can try adding a sound. If you run into problems, think about some of the creative problem-solving techniques that were discussed.
When complete, briefly comment on challenges or breakthroughs you encountered while completing the guided practice activity.
Pls help im giving 100 points for this i have this due in minutes
Answer:
u need to plan it out
Explanation:
u need to plan it out
Answer:
use the turn 1 degrees option and put a repeat loop on it
Explanation:
u can add sound in ur loop
A storm with a duration of about 24 hours resultsin the following hydrograph at a gaging station on a river. The flow was 52 cubic meters per second (cms) before the rain began. The drainage area above the gaging station is 1,450 square kilometers. Use the observed hydrograph to develop a 24-hour rainfall duration unit hydrograph for this watershed.
Time 0 6 12 18 24 30 36 42 48 54 60 66 72 78 84
(Hours)
Flow 52 52 55 56 97 176 349 450 442 370 328 307 280 259 238
(m3/s)
Time 90 66 102 108 114 120 126 132 138 144 155 156 162 168 176
(Hours)
(m3/s) 214 193 173 145 135 124 114 107 97 86 79 66 62 58 52
Answer:
attached below
Explanation:
Given data:
Gaged flow = 52 m^3 / sec
Depth covering drainage area = 1450 km^2
Develop a 24-hour rainfall duration unit hydrograph for the watershed using observed hydorgraph
Runoff flow = gaged flow - base flows
= 52 - 52 = 0 m^3/sec
For 18 hours time duration
Direct runoff volume ( Vr ) = ∑ ( QΔt1 )
where Δt = 6
∑Q = 3666 m^3/sec
hence Vr = Δt * ∑Q = 79185600 m^3
Next we will convert the Direct runoff volume to its equivalent depth covering the drainage area
= Vr / drainage area depth
= 79185600 / 1450000000 = 5.46 cm
Next we will find the unit hydrograph flows by applying the relation below
[tex]Q_{1.0cm} = Q_{5.46cm} (\frac{1.0cm}{5.46cm} )[/tex]
where 14m^3/sec = [tex]Q_{5.6cm}[/tex]
input value back to the above relation
[tex]Q_{1.0cm} = 2.57 m^3/sec[/tex]
Attached below is The remaining part of the solution tabulated below
and A graph of the unit hydorgraph for the given watershed
Note :
Base flow total = 1560
UH total = 671.30
If the sum of the two numbers is 4 and the sum of their squares minus three times their product is 76,find the number
Answer:
-2 and 6
Explanation:
Let "x" and "y" be 2 numbers.
The sum of the two numbers is 4. The mathematical expression is:
x + y = 4
y = 4 - x [1]
The sum of their squares minus three times their product is 76. The mathematical expression is:
x² + y² - 3 x y = 76 [2]
If we substitute [1] in [2], we get:
x² + (4 - x)² - 3 x (4 - x) = 76
x² + 16 - 8 x + x² - 12 x + 3 x² = 76
5 x² - 20 x - 60 = 0
We apply the solving formula for second order equations and we get x₁ = 6 and x₂ = -2.
If we replace these x values in [1], we get:
y₁ = 4 - x₁ = 4 - 6 = -2
y₂ = 4 - x₂ = 4 - (-2) = 6
As a consequence, one of the numbers is 6 and the other is -2.
Find the derivative of x
Answer:
this is your answer. if mistake don't mind.
Trace the following tree scan function and describe its action. template int treeFunc (tnode *t) int n = 0, left, right; if (t != NULL) { if (t->left != NULL) n++; if (t->right != NULL) n++; left = treeFunc (t->left); right = treeFunc (t->right); return n + left + right; else return 0; (a) identifies the number of leaf nodes in the tree (c) identifies the number of edges in the tree (b) identifies the number of nodes in the tree (d) identifies the depth of the tree.
The treeFunc function counts the number of nodes in a binary tree.
The function takes a pointer to the root of a binary tree as input.
It initializes a counter variable "n" to zero, and two variables "left" and "right" to store the results of recursive calls on the left and right subtrees, respectively.
If the root is not NULL, it checks whether the left and right children are NULL or not, and increments the counter "n" accordingly (if either child is not NULL, the node is not a leaf).
The function then recursively calls itself on the left and right children, storing the results in the variables "left" and "right".
Finally, it returns the sum of "n", "left", and "right", which gives the total number of nodes in the tree.
If the root is NULL, the function immediately returns 0.
Therefore, the correct answer is (b) identifies the number of nodes in the tree.
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Which of the following devices is a simple machine?
A.
an engine
B.
a pulley
C.
a motor
D.
a bicycle
E.
a crane
Answer:
A PULLY
Explanation:
HAD THIS ONE THAT IS THE CORRECT ANWSER
Answer:
The answer is B. a pulley
Explanation:
I hope I answered your question:)
A hoop of mass m and radius r starts from rest and rolls down an incline at an angle θ. The hoop’s inertia is given by IG = mr 2. The static friction coefficient is μs. Determine the acceleration of the center of mass aGx and the angular acceleration α. Assume that the hoop rolls without bouncing or slipping. Use two approaches to solve the problem: (a) Use the moment equation about the mass center G and (b) use the moment equation about the contact point P. (c) Obtain the frictional condition required for the hoop to roll without slipping.
The acceleration of the center of mass aGx is gsinθ/(1+I/mr^{2}), and the angular acceleration α is gsinθ/r(1+I/mr^{2}).
To find the acceleration of the center of mass aGx and the angular acceleration α of a hoop rolling down an incline at an angle θ, we can use two approaches. The first approach is to use the moment equation about the mass center G, which gives us aGx = gsinθ/(1+I/mr^{2}) and α = gsinθ/r(1+I/mr^{2}). The second approach is to use the moment equation about the contact point P, which gives us the same results. To ensure that the hoop rolls without slipping, we need to have a frictional force that is greater than or equal to the static friction coefficient μs times the normal force, which is equal to mgcosθ. Therefore, the required frictional condition is μs ≥ gcosθ/(1+I/mr^{2}).
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... is an actual sequence of interactions (i.e., an instance) describing one specific situation; a ... is a general sequence of interactions (i.e., a class) describing all possible ... associated with a situation. ... are used as examples and for clarifying details with the client. ... are used as complete descriptions to specify a user task or a set of related system features.
Answer:
ScenarioUse caseScenariosScenariosUse caseExplanation:
A scenario is an actual sequence of interactions (i.e., an instance) describing one specific situation; a use case is a general sequence of interactions (i.e., a class) describing all possible scenarios associated with a situation. Scenarios are used as examples and for clarifying details with the client. Use cases are used as complete descriptions to specify a user task or a set of related system features.
An air heater may be fabricated by coiling Nichrome wire and passing air in cross flow over the wire. Consider a heater fabricated from wire of diameter D=1 mm, electrical resistivity rhoe=10−6Ω⋅m, thermal conductivity k=25W/m⋅K, and emissivity ε=0.20. The heater is designed to deliver air at a temperature of T[infinity]=50∘C under flow conditions that provide a convection coefficient of h=250W/m2⋅K for the wire. The temperature of the housing that encloses the wire and through which the air flows is Tsur=50∘C. If the maximum allowable temperature of the wire is Tmax=1200∘C, what is the maximum allowable electric current I? If the maximum available voltage is ΔE=110V, what is the corresponding length L of wire that may be used in the heater and the power rating of the heater? Hint: In your solution, assume negligible temperature variations within the wire, but after obtaining the desired results, assess the validity of this assumption.
Solution :
Assuming that the wire has an uniform temperature, the equivalent convective heat transfer coefficient is given as :
[tex]$h_T= \epsilon \sigma (T_s+T_{surr})(T_s^2 +T^2_{surr})$[/tex]
[tex]$h_T= 0.20 \times 5.67 \times 10^{-8} (1473+323)(1473^2 +323^2)$[/tex]
[tex]$h_T=46.3 \ W/m^2 .K$[/tex]
The total heat transfer coefficient will be :
[tex]$h_T=(250+46.3) \ W/m^2 .K$[/tex]
[tex]$=296.3 \ W/m^2 .K$[/tex]
Now calculating the maximum volumetric heat generation :
[tex]$\dot {q}_{max}=\frac{2h_t}{r_0}(T_s-T_{\infty})$[/tex]
[tex]$\dot {q}_{max}=\frac{2\times 296.3}{0.0005}(1200-50)$[/tex]
[tex]$= 1.362 \times 10^{9} \ W/m^3$[/tex]
The heat generation inside the wire is given as :
[tex]$\dot{q} = \frac{I^2R}{V}$[/tex]
Here, R is the resistance of the wire
V is the volume of the wire
∴ [tex]$\dot{q} = \frac{I^2\left( \rho \times \frac{L}{A} \right)}{A \times L}$[/tex]
[tex]$=\frac{I^2 \rho}{\left(\frac{\pi}{4}D^2 \right)}$[/tex]
where, ρ is the resistivity.
[tex]$I_{max}= \left(\frac{\dot{q}_{max}}{\rho} \right)^{1/2} \times \frac{\pi}{4}D^2$[/tex]
[tex]$I_{max}= \left(\frac{1.36 \times 10^9}{10^{-6}} \right)^{1/2} \times \frac{3.14}{4}(1 \times 10^{-3})^2$[/tex]
= 28.96 A
Now considering the relation for the current flow through the finite potential difference.
[tex]$E=I_{max} \times R$[/tex]
[tex]$E=I_{max} \times \rho \times \frac{L}{A}$[/tex]
[tex]$L=\frac{AE}{I_{max} \ \rho}$[/tex]
[tex]$L=\frac{\frac{\pi}{4} \times (1 \times 10^{-3})^2 \times 110}{28.96 \times 10^{-6}}$[/tex]
= 2.983 m
Now calculating the power rating of the heater:
[tex]$P= E \times I_{max}$[/tex]
[tex]$P= 110 \times 28.96}$[/tex]
= 3185.6 W
= 3.1856 kW
An insulated closed piston–cylinder device initially contains 0.3 m3 of carbon dioxide at 200 kPa
and 27°C. A resistance heater inside the cylinder is turned on and supplied heat to the gas. As a
result, the gas expanded by pushing the piston up, until the volume doubled. During this process,
6
the pressure changed according to = 4, in which the constant 6 has units of kPa.m
a) Find the mass of the hydrogen in the tank in kg.
b) Determine the work done by the gas in kJ.
To solve this problem, we can use the ideal gas law and the equation for polytropic process.
What is ideal gas law ?The ideal gas law is a fundamental law of physics that describes the behavior of an ideal gas. It relates the pressure, volume, temperature, and number of particles of a gas using the following equation:
PV = nRT
a) First, we need to find the mass of the carbon dioxide in the tank. The ideal gas law is:
PV = mRT
where P is the pressure, V is the volume, m is the mass, R is the universal gas constant, and T is the temperature. Rearranging for the mass, we get:
m = PV / RT
Substituting the given values, we have:
m = (200 kPa)(0.3 m3) / [(0.287 kPam3/kgK)(27°C + 273.15)] = 3.87 kg
So the mass of the carbon dioxide in the tank is 3.87 kg.
b) To determine the work done by the gas during the process, we can use the equation for polytropic process:
P1V1^n = P2V2^n
where P1 and V1 are the initial pressure and volume, P2 and V2 are the final pressure and volume, and n is the polytropic index. Substituting the given values, we have:
(200 kPa)(0.3 m3)^n = (4)(0.6 m3)^n
Dividing both sides by (0.3 m3)^n and taking the logarithm of both sides, we get:
log(200) + nlog(0.3) = log(4) + nlog(0.6)
Solving for n, we get:
n = log(4/200) / log(0.6/0.3) ≈ 1.235
Using the polytropic work equation:
W = (P2V2 - P1V1) / (1 - n)
Substituting the given values, we have:
W = [(4 kPa)(0.6 m3) - (200 kPa)(0.3 m3)] / (1 - 1.235) = 233.7 kJ
So the work done by the gas during the process is 233.7 kJ.
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Determine (with justification) whether the following systems are (i) memoryless, (ii) causal, (iii) invertible, (iv) stable, and (v) time invariant. For invertibility, either find an inverse system or an example of two inputs that lead to the same output. Note that y[n] denotes the system output and x[n] denotes the system input.
a. y[n] = x[n] x[n-1] + [n+1]
b. y[n] = cos(x[n])
Answer:
a.
y[n] = x[n] x[n-1] x[n+1]
(i) Memory-less - It is not memory-less because the given system is depend on past or future values.
(ii) Causal - It is non-casual because the present value of output depend on the future value of input.
(iii) Invertible - It is invertible and the inverse of the given system is [tex]\frac{1}{x[n] . x[n-1] x[n+1]}[/tex]
(iv) Stable - It is stable because for all the bounded input, output is bounded.
(v) Time invariant - It is not time invariant because the system is multiplying with a time varying function.
b.
y[n] = cos(x[n])
(i) Memory-less - It is memory-less because the given system is not depend on past or future values.
(ii) Causal - It is casual because the present value of output does not depend on the future value of input.
(iii) Invertible - It is not invertible because two or more than two input values can generate same output values .
For example - for x[n] = 0 , y[n] = cos(0) = 1
for x[n] = 2[tex]\pi[/tex] , y[n] = cos(2[tex]\pi[/tex]) = 1
(iv) Stable - It is stable because for all the bounded input, output is bounded.
(v) Time invariant - It is time invariant because the system is not multiplying with a time varying function.