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patriot [66]
2 years ago
5

Two kilograms of air within a piston–cylinder assembly executes a Carnot power cycle with maximum and minimum temperatures of 80

0 K and 295 K, respectively. The heat transfer to the air during the isothermal expansion is 60 kJ. At the end of the isothermal expansion the volume is 0.4 m3. Assume the ideal gas model for the air. Determine the thermal efficiency, the volume at the beginning of the isothermal expansion, in m3, and the work during the adiabatic expansion, in kJ.

Engineering
2 answers:
Alekssandra [29.7K]2 years ago
6 0

Answer:

a.) Thermal efficiency = 0.37

b.) Volume = 0.229 m^3

c.) Work done = 1393.3 kJ

Explanation: Please find the attached files for the solution

creativ13 [48]2 years ago
6 0

Answer:

thermal efficiency, η=  0.63125

volume at the beginning of the isothermal expansion, V1 = 0.34011 m3

work during the adiabatic expansion, in kJ = 766.59 KJ

Explanation:

<u>To determine the thermal efficiency</u>

The thermal efficiency of a heat engine gives an estimation of the amount of heat energy converted to work in the engine.

Thermal efficiency is given by: η= 1-  (Tc/Th)

where, Tc= ambient temperature or the minimum temperature

            Th=  maximum temperature

from the given data:

minimum temperature = 295 K

maximum temperature =  800 K

η= 1-  (295/800)

η=  0.63125

<u>To determine the volume at the beginning of the isothermal expansion, in m3</u>

We know,  ΔU = Q − W.

where,  ΔU is the change in internal energy of the system.

Q= mRT In (V2/V1)

Where, V1 = volume at the beginning of the isothermal expansion

             V2 = = volume at the end of the isothermal expansion

Therefore, V1 = V2 / (Q/mRT)

V1= 0.4/ ((60000/ (2 x 287 x 800))

V1 = 0.34011 m3

where, isothermal expansion given is 60 kJ

             isothermal expansion the volume given is 0.4 m3

<u>To determine the work during the adiabatic expansion, in kJ.</u>

Work during the adiabatic process is given by

W = − ΔU

where,  ΔU is the change in internal energy of the system

W at the first and second process = - 2 x 759 ( 295 - 800)

= 766590J = 766.59 KJ

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Answer:

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Explanation:

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temperature T1 = 270 K

velocity = 180 m/s

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solution

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so we write here energy balance equation that is

0 = m (h1-h2) + m ×  (\frac{v1^2}{2}-\frac{v2^2}{2})   .....................1

so it will be

h1 + \frac{v1^2}{2} = h2 + \frac{v2^2}{2}      .....................2

put here value by using ideal gas table

and here for temperature 270K

h1 = 270.11 kJ/kg

270.11 + \frac{180^2\times \frac{1}{1000}}{2} = h2 + \frac{48.4^2\times \frac{1}{1000}}{2}  

solve it we get

h2 = 285.14 kJ/kg

so by the ideal gas table we get

T2 = 285 K

4 0
3 years ago
A 360 kg/min stream of steam enters a turbine at 40 bar pressure and 100 degrees of superheat. The steam exits the turbine as a
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Where the velocity is highest in the radial direction? Why?
posledela

Answer:

In the center and directed away from it.

Explanation:

The direction along the radius and directed away from the center is known as radial direction.

The velocity is highest in the radial direction pointing away from the center, this is because of the reason that  when the particle executes its motion in the direction that is radial, then it is not acted upon by any force that opposes the motion of the particle and thus there is no obstruction to the velocity of the particle and it is therefore, the highest in the radial direction.

8 0
3 years ago
Annealing is a process by which steel is reheated and then cooled to make it less brittle. Consider the reheat stage for a 100-m
zvonat [6]

Answer:

T = 858.25 s

Explanation:

Given data:

Reheat stage for a 100-mm-thick steel plate ( 7830 kg/m3,  c 550 J/kg K, k 48 W/m K),

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Final temperature = 550 c

convection coefficient  = 250 w/m^2 k

products combustion temp = 800 c

calculate how long the plate should be left in the furnace ( to attain 550 c )

first calculate/determine the Fourier series Number ( Fo )

\frac{T_{0}-T_{x}  }{T_{1}-T_{x}  } = C_{1} e^{(-0.4888^{2}*Fo )}

= 0.4167 = 1.0396e^{-0.4888*Fo}

therefore Fo =  3.8264

Now determine how long the plate should be left in the furnace

Fo = (\frac{k}{pc_{p} } ) ( \frac{t}{(L/2)^2} )

k = 48

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L = 0.1

Input the values into the relation and make t subject of the formula

hence t = 858.25 s

8 0
3 years ago
Determine the angular acceleration of the uniform disk if (a) the rotational inertia of the disk is ignored and (b) the inertia
lukranit [14]

Answer:

α = 7.848 rad/s^2  ... Without disk inertia

α = 6.278 rad/s^2  .... With disk inertia

Explanation:

Given:-

- The mass of the disk, M = 5 kg

- The right hanging mass, mb = 4 kg

- The left hanging mass, ma = 6 kg

- The radius of the disk, r = 0.25 m

Find:-

Determine the angular acceleration of the uniform disk without and with considering the inertia of disk

Solution:-

- Assuming the inertia of the disk is negligible. The two masses ( A & B )  are hung over the disk in a pulley system. The disk is supported by a fixed support with hinge at the center of the disk.

- We will make a Free body diagram for each end of the rope/string ties to the masses A and B.

- The tension in the left and right string is considered to be ( T ).

- Apply newton's second law of motion for mass A and mass B.

                      ma*g - T = ma*a

                      T - mb*g = mb*a

Where,

* The tangential linear acceleration ( a ) with which the system of two masses assumed to be particles move with combined constant acceleration.

- g: The gravitational acceleration constant = 9.81 m/s^2

- Sum the two equations for both masses A and B:

                      g* ( ma - mb ) = ( ma + mb )*a

                      a =  g* ( ma - mb ) / ( ma + mb )

                      a = 9.81* ( 6 - 4 ) / ( 6 + 4 ) = 9.81 * ( 2 / 10 )

                      a = 1.962 m/s^2  

- The rope/string moves with linear acceleration of ( a ) which rotates the disk counter-clockwise in the direction of massive object A.

- The linear acceleration always acts tangent to the disk at a distance radius ( r ).

- For no slip conditions, the linear acceleration can be equated to tangential acceleration ( at ). The correlation between linear-rotational kinematics is given below :

                     a = at = 1.962 m/s^2

                     at = r*α      

Where,

           α: The angular acceleration of the object ( disk )

                    α = at / r

                    α = 1.962 / 0.25

                    α = 7.848 rad/s^2                                

- Take moments about the pivot O of the disk. Apply rotational dynamics conditions:

             

                Sum of moments ∑M = Iα

                 ( Ta - Tb )*r = Iα

- The moment about the pivots are due to masses A and B.

 

               Ta: The force in string due to mass A

               Tb: The force in string due to mass B

                I: The moment of inertia of disk = 0.5*M*r^2

                   ( ma*a - mb*a )*r = 0.5*M*r^2*α

                   α = ( ma*a - mb*a ) / ( 0.5*M*r )

                   α = ( 6*1.962 - 4*1.962 ) / ( 0.5*5*0.25 )

                   α = ( 3.924 ) / ( 0.625 )

                   α = 6.278 rad/s^2

6 0
3 years ago
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