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Svetradugi [14.3K]
4 years ago
13

Air within a piston cylinder assembly executes a Carnot refrigeration cycle between hot and cold reservoirs at TH=600 K and TC=3

00 K, respectively. The magnitude of the heat transfer rejected to the high temperature reservoir is 250 kJ per kg of air. The pressure at the start of the isothermal expansion is 325 kPa. The air can be modeled as an ideal gas with constant specific heat (k=1.4). For the air as a system, determine
a. (5) the coefficient of performance.
b. (5) the net work input to the cycle in kJ/kg.
c. (10) the Pv and Ts diagrams for the cycle with arrows showing the directions of the processes.
You may answer parts (a) and (b) in the response box. Part (c) and your calculations supporting.(a) and (b) must be included in your uploaded response file.

Engineering
1 answer:
Nataly [62]4 years ago
5 0

Answer:

See explaination

Explanation:

for a reverse carnot cycle T-S diagram is a rectangle which i have shown

net work for a complete cycle must be equal to net heat interaction.

Kindly check attachment for the step by step solution of the given problem.

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A coil having resistance of 7 ohms and inductance of 31.8 mh is connected to 230v,50hz supply.calculate 1. The circuit current 2
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(1) The current in the circuit is 18.87 A,

(2) The phase angle is 54.97°

(3) The power factor is 0.574

(4) The power consumed is 2491.2 W

(1) To calculate the current in the circuit, first, we need to find the overall impedance of the circuit.

We can calculate the overall impendence of the circuit using the formula below.

  • Z = √[R²+(2πfL)²]........................ Equation 1

Where:

  • R = resistance of the coil
  • f = Frequency
  • L = Inductance of the coil
  • Z = Overall impedance of the circuit

From the question,

Given:

  • R = 7 ohms
  • L = 31.8 mH = 0.0318 H
  • f = 50 Hz
  • π = 3.14

Substitute these values into equation 1

  • Z = √[7²+(2×3.14×50×0.0318)²]
  • Z = √(49+99.7)
  • Z = √(148.7)
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Therefore we use the formula below to calculate the current in the circuit.

  • I = V/Z.................. Equation 2

Where:

  • V = Voltage
  • I = current in the circuit.

Given:

  • V = 230 V.

Substitute into equation 2

  • I = 230/12.19
  • I = 18.87 A

(2) To calculate the phase angle, we use the formula below.

  • ∅ = tan⁻¹(2πfL/R)............... Equation 3

Where:

  • ∅ = Phase angle.


Substitute into equation 3

  • ∅ = tan⁻¹(2×3.14×50×0.0318/7)
  • ∅ = tan⁻¹(9.9852/7)
  • ∅ = tan⁻¹(1.426)
  • ∅ = 54.97°

(3) To calculate the power factor, we use the formula below.

  • pf = cos∅............ Equation 4

Where:

  • pf = power factor.

Substitute the value of ∅ into equation 4

  • pf = cos(54.97°)
  • pf = 0.574.

(4) And Finally to calculate the power consumed we use the formula below.

  • P = V×I×pf................ Equation 5

Where:

  • P = The power consumed

Substitute the values into equation 5

  • P = 230(18.87)(0.574)
  • P = 2491.22 W


Hence, (1) The current in the circuit is 18.87 A, (2) The phase angle is 54.97° (3) The power factor is 0.574 (4) The power consumed is 2491.2 W

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