Answer:
[tex]e^{ix} = cosx + i sinx[/tex]
Explanation:
In mathematics, Euler's formula is an equation in complex analysis, that gives a relationship between an exponential factor and the trigonometric functions.
The Euler equation is:
[tex]e^{ix} = cosx + i sinx[/tex]
Here,
e - base of the natural logarithm
i - imaginary unit
x - argument given in radians
sin , cos - trigonometric functions sine and cosine respectively.
A rigid, sealed tank initially contains 2000 kg of water at 30 °C and atmospheric pressure. Determine: a) the volume of the tank (m3 ). Later, a pump is used to extract 100 kg of water from the tank. The water remaining in the tank eventually reaches thermal equilibrium with the surroundings at 30 °C). Determine: b) the final pressure (kPa).
Given:
mass of water, m = 2000 kg
temperature, T = [tex]30^{\circ}C[/tex] = 303 K
extacted mass of water = 100 kg
Atmospheric pressure, P = 101.325 kPa
Solution:
a) Using Ideal gas equation:
PV = m[tex]\bar{R}[/tex]T (1)
where,
V = volume
m = mass of water
P = atmospheric pressure
[tex]\bar{R} = \frac{R}{M} [/tex]
R= Rydberg's constant = 8.314 KJ/K
M = molar mass of water = 18 g/ mol
Now, using eqn (1):
[tex]V = \frac{m\bar{R}T}{P}[/tex]
[tex]V = \frac{2000\times \frac{8.314}{18}\times 303}{101.325}[/tex]
[tex]V = 2762.44 m^{3}[/tex]
Therefore, the volume of the tank is [tex]V = 2762.44 m^{3}[/tex]
b) After extracting 100 kg of water, amount of water left, m' = m - 100
m' = 2000 - 100 = 1900 kg
The remaining water reaches thermal equilibrium with surrounding temperature at T' = [tex]30^{\circ}C[/tex] = 303 K
At equilibrium, volume remain same
So,
P'V = m'[tex]\bar{R}[/tex]T'
[tex]P' = \frac{1900\times \frac{8.314}{18}\times 303}{2762.44}[/tex]
Therefore, the final pressure is P' = 96.258 kPa
Sketch and label a simple reheat cycle along with the appropriate T-s diagram?
Answer:
A reheat cycle is used to increase the overall efficiency of the power plant.
Explanation:
The Reheat cycle is used --
1. to increase the efficiency of the turbine
2. to maintain the quality of the steam
3. to provide higher pressure ratio
The reheat cycle is used to to increase the net work output of the power plant.In reheat cycle, two turbines , one low pressure turbine and one high pressure turbine is used to increase the efficiency. The main purpose of the reheat cycle is to maintain the quality of the steam to 0.85 at the exit of the turbine.
The figure given below shows a reheat rankine cycle.
In the cycle,
Process 1-2 is high pressure turbine
Process 2-3 is the reheater
Process 3-4 is the low pressure turbine
Process 4-5 is condenser
Process 5-6 is pump
Process 6-1 is boiler
A reheat rankine cycle is 30 -40% efficient than a simple rankine cycle.
_____What is matrix in tungsten carbide cutting tool? a)- Chromium b)- Manganese c)- Cobalt d)- Aluminum
Answer:
The correct option is C) Cobalt
Explanation:
The cemented carbides are hard substances which are extensively used as cutting tools materials. In the cemented carbides, substances like tungsten-carbide are used as aggregates.
A tungsten carbide- cobalt cutting tool is a metal matrix composite, in which the tungsten carbide is the aggregate and the cobalt is the matrix.
Therefore, in the tungsten carbide cutting tool, cobalt is used as the matrix.
What is the Principle of Entropy Increase?
Answer and Explanation:
The increase in entropy principle is defined as the process in which the total change in entropy of system with its adiabatic surroundings is always positive or equal to zero. The increase in entropy mostly takes place when a solid becomes liquid because randomness is increases when solid becomes liquid so entropy is also increases.
example of increase of entropy is when solid burns and become ash, ice melting
What is flow energy? Do fluids at rest possess any flow energy?
Flow energy is the energy possessed by a fluid due to its motion, which is quantified by kinetic energy density. Based on Bernoulli's equation, fluids at rest do not have flow energy but can have potential energy. The total mechanical energy of a fluid includes potential and kinetic energy components.
Explanation:Flow energy refers to the energy that fluid possesses due to its motion. This form of energy can be described by kinetic energy density, which is part of the total mechanical energy in a flowing fluid. According to Bernoulli's equation, the total mechanical energy of a fluid is composed of potential energy and kinetic energy. The kinetic energy of the fluid relates to its velocity and is expressed as (1/2)ρV^2, where ρ is the density of the fluid and V is the fluid velocity. On the other hand, fluids at rest do not possess flow energy or kinetic energy related to movement, but they can still have potential energy due to their position.
According to conservation of energy principles, the work done by the fluid's pressure changes the fluid's kinetic and potential energies, per unit volume. No additional flow energy is present in a fluid at rest; however, it may still exert pressure at the bottom of a container or well due to its potential energy.
Describe the steps involved in accomplishing a life-cycle cost analysis (LCCA). I have listed the steps. just describe. a)-Operational Performance. b)-Salvage externalities c)- Value vs. Risk d)- Initial expenditure e)- Maintenance implications
Explanation:
a). Operational Performance
It is defined as the parameter that describes the percentage of accuracy of performing an operation or carrying out an activity.
b). Salvage externalities
Salvage in Life cycle cost analysis is a process of estimating the value of the remaining assets in the organisation,.
c). Value Vs Risk
When we take risk in doing any activity we know the value of accomplising the activity. So value relates directly with risk. When the value of a certain task is high, the risk involve in it is also high.
d). Initial expenditure
Initial expenditure is nothing but the cost involve in starting a particular acitvity or task at the starting phase.
e). Maintenance implications
It lays emphasis in maintaining the cost of every possible parameters that are involve in the activity. It includes labour, machines, positions, energy, facilities, etc.
Consider three identical items in parallel. What is the system reliability if each item has a reliability of 98%?
Answer:
Reliability of system = 99.9992%
Explanation:
Given Reliability of item = 98%
therefore probability of failure = 100%-98% =2%
For system in parallel the probability of failure is product of individual probabilities of items
thus
[tex]Probabilityfail_{system}=p_{1}\times p_{2}\times p_{3}\\\\Probabilityfail_{system}=0.02^{3}=0.000008\\\\Realibility_{system}=100- Probabilityfail_{system}\\\\Realibility_{system}=99.9992%[/tex]
-Pure substance at sublimation line exist as a mixture of liquid and solid(____)
Answer:
False
Explanation:
A graphical representation of transition of substance's physical state under various temperature and pressure conditions is known as phase diagram.
A typical phase diagram usually consists of:
(A) Fusion curve - The curve that represents that the solid and the liquid state exists in the equilibrium with each other is called fusion curve.
(B) Vaporization curve - The curve that represents that the liquid and the gaseous state exists in the equilibrium with each other is called fusion curve.
(C) Sublimation curve - The curve that represents that the solid and the gaseous state exists in the equilibrium with each other is called fusion curve.
(D) Triple point - This is a point in the phase diagram in which all the three state exists in equilibrium.
Thus, for a pure substance, sublimation line exist as a mixture of solid and gas. The statement is false.
An actual vapour compression system comprises following process represents a. 1-2 Compression process b. 2-3 Condens 1 (or heat rejection from the condenser) c. 3-4 Irreversible expansion d. 4-1 Evaporation (or) heat addition to the evaporator Sketch the processes on T-S diagram.
Answer:
Explanation:
The deatailed diagram of VCRS is given below such
1-2=Isentropic compression in which temperature increases at constant entropy
2-3=Isobaric heat rejection i.e. heat rejected at constant pressure(condensation)
3-4=Irreversible expansion or throttling in which enthalpy remains constant
4-1=Isobaric heat addition(Evaporation)
Define the Static Balancing.
Answer: Static Balancing is when a stationary object has the the ability to balance because its core centre of gravity is on the axis of rotation.
What is the uncertainty in position of an electron of an atom if there is t 2.0 x 10' msec uncertainty in its velocity? Use the reduced Planck's constant and electron mass 9.19 x 103 kg.
Answer:
18931.4
Explanation:
Given : velocity of the electron = 2.0 [tex]\times[/tex]10
mass of the electron = 9.19[tex]\times[/tex] 103
we know that reduced planks constant, h = 6.5821[tex]\times[/tex] [tex]10^{-16}[/tex] eV s
We know from uncertainity principle,
[tex]\Delta \textup{x}.\Delta \textup{v} = \frac{h}{\dot{m}}[/tex]
[tex]\Delta \textup{x} = \frac{h}{\dot{m}\times \Delta \textup{v}}[/tex][tex]\Delta \textup{x} = \frac{6.5821\times 10^{-16}}{9.19\times 103\times 2.0\times 10}[/tex]
[tex]\Delta \textup{x}[/tex] = 18931.4 m
Hence, uncertainty in position of the electron is 18931.4
Burn rate can be affected by: A. Variations in chamber pressure B. Variations in initial grain temperature C. Gas flow velocity D. All of the above
Answer: D) All of the above
Explanation:
Burn rate can be affected by all of the above reasons as, variation in chamber pressure because the pressure are dependence on the burn rate and temperature variation in initial gain can affect the rate of the chemical reactions and initial gain in the temperature increased the burning rate. As, gas flow velocity also influenced to increasing the burn rate as it flowing parallel to the surface burning. Burn rate is also known as erosive burning because of the variation in flow velocity and chamber pressure.
What is a Mollier diagram?
Answer: Mollier diagram is the diagram or graph representing the relation established between enthalpy ,air, moisture and temperature.
Explanation: Mollier graph represents the basic thermodynamic properties along with terms of enthalpy and entropy. The factors like air, moisture , temperature etc. are plotted on the graph which makes it easy to understand. It is used in the field building designers and engineer.They are usually plotted for the gases with purity with general pressure and temperature.
Are spheroidized steels considered as composite? If so, what is the dispersed phase a)- No b)- Yes, Chromium Carbides c)- Yes, Iron Carbides d)- Yes, Intermetallic Compounds
Answer: c)-Yes, spheroidized steel are considered as composite.the dispersed phase is iron carbide.
Explanation: Spheroidized steel are the alloy that have iron as the basic part that have been heat treated to increase their ductility and malleability property .They are considered as composite because they are made up of iron alloys. The heat treatment is usually for the carbon steel and so the dispersed phase that is obtained is iron carbide.
Heat in the amount of 100 kJ is transferred directly from a hot reservoir at 1200 K to a cold reservoir at 600 K. Calculate the entropy change of the two reservoirs and determine if the increase of entropy principle is satisfied.
Solution:
Given:
[tex]T_{H}[/tex] = 1200 K
[tex]T_{L}[/tex] = 600 K
Q = 100 kJ
The Entropy change of the two reservoirs is given by the sum of entropy change of each reservoir system and is given by the formula:
[tex]\Delta s = \frac{-Q}{T_{H}}+\frac{Q}{T_{L}}[/tex]
[tex]\Delta s = \frac{Q(T_{L}-T_{_{H}})}{T_{H}T_{L}}[/tex]
[tex]\Delta s = \frac{-100(600-1200)}{1200\times 600}[/tex]
[tex]\Delta s = 0.0833kJ/K
Since, the change in entropy is positive and according to the Increase in entropy principle, for any process the total change in entropy of a system is always greater than or equal to zero (with its enclosing adiabatic surrounding).
Therefore, the entropy principle is satisfied.
A composite material is a mix of two different materials such as ceramics and metals fused together to the atomic level to form another substance with more improved propertied.a)-True b)-False
Answer:
The correct option is (A) TRUE
Explanation:
A composite material is the material having characteristics that are improved and different from the constituting materials. A composite material is produced by combining two or more materials. The constituting materials have significantly different physical or chemical properties.
Some of the composite materials include-Ceramic matrix composites, Metal matrix composites etc.
A ceramic matrix composite is formed by embedding ceramic fibers in a ceramic matrix.
Also, a tungsten carbide- cobalt is a metal matrix composite, in which the tungsten carbide and cobalt metal matrix are fused together.
Therefore, the given statement: A composite material is a mix of two different materials that are fused together on the atomic level to form a new substance with improved properties is TRUE.
Just-in-time delivery is not an important component of Lean manufacturing. a)- True b)- False
Answer:
False
Explanation:
Just-in-time manufacturing means that production is done when there is demand. It is a pull system which means that demand dictates production. Lean manufacturing is method of production which aims to reduce the seven types of waste which are
Logistics
Inventory
Motion of objects during manufacturing
Unnecessary delay
Producing more than demand
Over Processing of goods
Malfunctioning items.
Here it can be seen that Producing more than demand is a waste. This can be reduced by Just in Time manufacturing.
______number can be used to describe the relative growth of the hydraulic boundary layer and the thermal boundary layer. a) Reynolds b) Stanton c) Nusselt d) Prandtl e) Fourier
Answer: d) Prandtl number
Explanation: Prandtl number is basically defined as the ratio between the fluid's viscosity to the thermal conductivity.It doesn't have any sort of dimension. The fluids which are discovered with the small Prandtl numbers are considered as good fluids as they have a smooth rate of flow and as the number increases the fluid are not considered as reliable. Thus,option (d) is the correct option.
A refrigeration cycle rejects Qn 500 Btu/s to a hot reservoir at 540 R, while receiving c200 Btu/s at 240°R. This refrigeration cycle a)- is internally reversible b)- is irreversible c)- is impossible d)- cannot be determined
Answer:
(b) Irreversible cycle.
Explanation:
Given;
[tex]T_2=540R ,Q_2= 500 Btu/s ,T_1=240 R ,Q_1= 200 Btu/s [/tex]
To find the validity of cycle
[tex]\oint _R\frac{dQ}{T}\leq0[/tex]
If it is zero then cycle will be reversible cycle and if it is less than zero then cycle will be irreversible cycle.These are possible cycle.
If it is greater than zero ,then cycle will be impossible .
Now find
[tex]\dfrac{Q_1}{T_1}-\dfrac{Q_2}{T_2}=\dfrac{200}{240}-\dfrac{500}{540}[/tex]
[tex]\dfrac{Q_1}{T_1}-\dfrac{Q_2}{T_2}[/tex]= -0.09
It means that this cycle is a irreversible cycle.
A Carnot machine operates with 25% efficiency, whose heat rejection reservoir temperature is 300K. Determine the temperature at which the machine absorbs heat.
Answer:
The temperature at which observed heat is 400 K
Explanation:
Given data:
rejection reservoir temperature at exit [tex]T_{L}[/tex] is 300 k
the efficiency of a engine is η = 25%
we know that efficiency of Carnot is given as
[tex]\eta = (1-\frac{T_{L}}{T_{H}})*100[/tex]
Putting all value to obtained temperature at which observed heat
[tex]0.25 = (1-\frac{300}{T_{H}})[/tex]
[tex]T_{H}[/tex] = 400 K
The purifier is a device in a)- The air separation plant b)- steam power plant c)-- fuel cell d)- refrigerator
Answer:
a). Air separation plant
Explanation:
The purifier is a device that removes the pollutants or air contaminants from air to improve the air quality in a given space.
There are basically two techniques or ways by which the air purifier makes the air contaminants free. This two techniques are active and passive.
Active air purifiers : negatively charged ions are released to the atmosphere which sticks the pollutants to the surface.
Passive air purifiers : They use air filters to eliminate pollutants and are more efficient than an active air purifiers.
Answer:
(A) Air separation plant
Explanation:
Purifier is used in air separation plant to purify the air main work of purifier is to remove the pollutants particles from the air and make the air fresh.
On the other hand it has no use team power pant because in steam power plant we don't need to purify the steam and also not used in fuel cell and refrigerator
So purifiers are used in the air separation plant.
Define the various properties and constraints that ensure weldability/joinability.
Answer:
Listed Below
Explanation:
Weldability which is also known as joinability is defined as the ease with which a material can be welded without producing any other effect .
Some factors which affect weldability are
1.Melting point of metal
Higher the melting point lower will be the weldability.2.Thermal conductivity
Materials with higher thermal conductivity are difficult to join.3.Reactivity
If the material reacts with surroundings like water or air, it is difficult to weld.4.Coefficient of thermal expansion(α)
Higher the thermal expansion lower will be the weldability.5.Surface condition
The material with dirty surface is difficult to weld for example if a surface has oxide layer on it it become difficult to weld it.What i s the value of a capacitor with 250 V applied and has 500 pC of charge? (a) 200 uF (b) 0.5 pF (c) 500 uF (d) 2 pF
Answer:
(d) 2 pF
Explanation: the charge on capacitor is given by the expression
Q=CV
where Q=charge
C=capacitance
V=voltage across the plate of the capacitor
here we have given Q=500 pF, V=250 volt
using this formula C=[tex]\frac{Q}{V}[/tex]
=500×[tex]10^{-12}[/tex]×[tex]\frac{1}{250}[/tex]
=2×[tex]10^{-12}[/tex]
=2 pF
Injector orifice patterms and size will affect propellant mixing and distribution. a)-True b)-False
Answer: True
Explanation: Injector orifice is the factor which describes the size of the opening of the injector .There are different pattern and size of the opening for the injector which affects the mixture of the chemical substance that is used for the production of the energy that is known as propellant.
The pattern and size of the orifice will define the variation in the amount of energy that could be produced.Thus the statement given is true.
What do you think are the advantages and disadvantages of isothermal constant volume high extension cycle? And how efficient do you think it can be?
Answer Explanation :
ADVANTAGES OF ISOTHERMAL PROCESS
EASE OF MAINTENANCE: there is absence of direct contact between the combustible gas mixture and all moving part in this process LESS NOISE : These engines does not have valves so it is very simple in construction and produce less noiseBETTER PERFORMANCE : these engine have better performance than other enginesLOW TEMPERATURE : these engine can work on low temperature which is also an advantageDISADVANTAGES OF ISOTHERMAL PROCESS :
GREATER VOLUME AND GREATER WEIGHT: These engine require large volume and large weightSLOWER START: In this process the engine have very slower start which is a disadvantage HIGHER ECONOMIC COST : In this process we need more money this is also an disadvantage
A motor is rated to deliver (output) 2.5 hp at 120 VDC. If the motor runs on 120 V and is 75% efficient, how many watts does it draw from the power line (input)? ( input power is always greater than output power, and remember to use a horse power conversion: 1hp =746 (watts) (a) 3.33 W (b) 1399 W (c) 1679 w (d) 2072 W (e) 2487 W
Answer:
(e) 2487 W
Explanation:
Given data
voltage = 120 V
power = 2.5 hp
efficiency = 75%
To find out
watts draw from the power line
solution
we calculate efficiency by given formula
efficiency = ( output / input ) × 100 ............1
we know our output is 2.5 hp = 2.5 × 746 = 1865 W
and efficiency is 75% = 0.75
put these value in equation 1 and find out input power
power = ( 1865 / 0.75 )
power = 2486.66 W
so our answer is (e) 2487 W
For high temperature deformation, the bigger the gran sine, the higher the creep rate. a)-True b)- False
Answer:
The given statement is False.
Explanation:
This is because at high temperature the creep rate depends on grain boundary area, increasing with an increase in grain boundary area thus decreasing the grain size. Thus at higher temperatures, grain size has opposite effect , the bigger the grain size the slower the slower is the creep rate, the larger the grain boundary area.
Answer:
a
Explanation:
a
The number-average molecular weight of a poly(styrene-butadiene alternating copolymer is 1,350,000 g/mol; determine the average number of styrene and butadiene repeat units per molecule.
To find the average number of styrene and butadiene units in a poly(styrene-butadiene) copolymer with Mn of 1,350,000 g/mol, add the molecular weights of styrene and butadiene to get the molecular weight of the repeat unit (158.24 g/mol) and divide Mn by this number to get approximately 8530 repeat units, which includes about 4265 of each monomer type.
Explanation:To calculate the average number of styrene and butadiene repeat units per molecule for a poly(styrene-butadiene) copolymer with a number-average molecular weight (Mn) of 1,350,000 g/mol, we need the molecular weights of the monomer units. The molecular weight of styrene (C8H8) is approximately 104.15 g/mol, and the molecular weight of butadiene (C4H6) is approximately 54.09 g/mol. Since the copolymer is alternating, each repeat unit consists of one styrene and one butadiene unit.
To find the total molecular weight of the repeat unit, we add the molecular weights of styrene and butadiene: 104.15 g/mol + 54.09 g/mol = 158.24 g/mol. Dividing the number-average molecular weight of the copolymer by the molecular weight of the repeat unit gives us the average number of repeat units per molecule: 1,350,000 g/mol \/ 158.24 g/mol \approximately 8530 repeat units\.
The average number of styrene units per molecule will be approximately 4265, and the same for butadiene, since there is one of each in every repeat unit in an alternating copolymer structure.
In a steady flow device, the properties of the system remains constant with time. a)True b) False
Answer:
True
Explanation:
By definition of steady flow we have
[tex]\frac{\partial f(x,y,z,t) }{\partial t}=0[/tex]
where f(x,y,z,t) is any property of the system under consideration
=> f(x,y,z,t) = constant
What does WCS stand for? A. Western CAD System B. Worldwide Coordinate Sectors C. World Coordinate System D. Wrong CAD Settings
Answer:
The correct answer is C. World Coordinate System
Explanation:
The World Coordinate System has to do with that coordinate system which is fixed in the activities of the CADing. There is a default system in which we can refer to them as soon as we want to manipulate the objects and add new elements.