Answer:
a. Composition of Vector.
Explanation:
When a bird flies in the air, it stretches its wings into air and this movement helps it move in a certain direction. This is an example of composition of vector. Air strikes the wings in opposite direction and bird wing movement helps it move against the wind.
Answer:
L = Henry
C = Farad
Explanation:
The electrical parameter represented as L is the inductance whose unit is Henry(H).
The electrical parameter represented as C is the inductance whose unit is Farad
Resonance frequency occurs when the applied period force is equal to the natural frequency of the system upon which the force acts :
To obtain :
At resonance, Inductive reactance = capacitive reactance
Equate the inductive and capacitive reactance
Inductive reactance(Xl) = 2πFL
Capacitive Reactance(Xc) = 1/2πFC
Inductive reactance(Xl) = Capacitive Reactance(Xc)
2πFL = 1/2πFC
Multiplying both sides by F
F * 2πFL = F * 1/2πFC
2πF²L = 1/2πC
Isolating F²
F² = 1/2πC2πL
F² = 1/4π²LC
Take the square root of both sides to make F the subject
F = √1 / √4π²LC
F = 1 /2π√LC
Hence, the proof.
Answer:
W=-109.12 kJ/kg
Q=-76.34 kJ/kg
Explanation:
The needed work W we will calculate by using the work equation for polytropic process and the heat transfer Q we will calculate by using the energy balance equation.
Before the calculations we first need to determine the final temperature T2. We will do that by using the given initial temperature T1 = 10°C, the given initial p_1 = 120 kPa and final p_2 = 800 kPa pressure and the polytropic index n = 1.2. Before the calculation we need to express the temperature in K units.
T1 = 10°C + 273 K = 283 K
T2 = ((p_2/p_1)^(n-1)/n)* T1
T2 = 388 K
Now we can use the heat capacity C_v, = 0.3122 kJ /kg K and the temperatures T1 and T2 to determine the change in internal energy ΔU.
ΔU = C_v*(T2-T1)
ΔU = 32.78 kJ/kg
to determine the work we will also need the initial v1 and final v2 specific volume. The initial specific volume v1 we can determine from the ideal gas equation. For the calculation we will need the initial pressure p_1, temperature T1 and the specific gas constant R = 0.2081 kJ /kg K.
v1=R*T1/p_1
v1=0.4908 m^3/kg
For the final specific volume we need to replace the initial temperature and pressure with the final.
v2=R*T2/p_2
v2=0.1009 m^3/kg
The work W is then:
W=p_2*v2-p_1*v1/n-1
W=-109.12 kJ/kg
The heat transfer Q we can calculate form the energy balance equation. For the calculation we will need the calculated work W and the change in internal energy ΔU.
Q=W+ΔU
Q=-76.34 kJ/kg
Answer:
T2 ( final temperature ) = 576.9 K
a) 853.4 kJ/kg
b) 1422.3 kJ / kg
Explanation:
given data :
pressure ( P1 ) = 90 kPa
Temperature ( T1 ) = 30°c + 273 = 303 k
P2 = 450 kPa
Determine final temperature for an Isentropic process
----------- ( 1 )
T2 = 303 
= 576.9K
Work done in a piston-cylinder device can be calculated using this formula
------- ( 2 )
where : cv = 3.1156 kJ/kg.k for helium gas
T2 = 576.9K , T1 = 303 K
substitute given values Back to equation 2
= 853.4 kJ/kg
work done in a steady flow compressor can be calculated using this
where : cp ( constant pressure of helium gas ) = 5.1926 kJ/kg.K
T2 = 576.9 k , T1 = 303 K
substitute values back to equation 3
= 1422.3 kJ / kg
