Chapter 3 Tutorials

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Chapter 3 Tutorials
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• Problem 1
• When is the energy crossing the boundaries of a
  closed system heat and when is it work?
• Answer
• The form of energy that crosses the boundary of a
  closed system because of temperature difference
  is heat all other forms are work.

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• Problem 2
• When is an adiabatic process? What is an
  adiabatic system?
• Answer
• An adiabatic process is a process during which
  there is no heat transfer. A system that does not
  exchange any heat with its surrounding is an
  adiabatic system.

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• Problem 3
• On a P-v diagram, what does the area under the
  process curve represent?
• Answer
• It represents the boundary work for
  quasi-equilibrium processes.

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• Problem 4
• A mass of 5 kg of saturated water vapor at 200
  kPa is heated at constant pressure until the
  temperate reaches 300oC. Calculate the work done
  by the steam during the process.
• Solution
• Pressure remains constant during the process.
• Specific volume at initial and final states.
• Mass of water vapor, m 5 kg

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• Initial state
• P1200kPa, saturated vapor
• v1vg_at_p1200kPa0.8857m3/kg From A-5
• Final state
• P2200kPa, T2300OC (Superheated)
• v2 1.3162 m3/kg From A-6

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• Problem 5
• A frictionless piston-cylinder device initially
  contains 200L of saturated liquid refrigerant
  134a. The piston is free to move, and its mass is
  such that it maintains a pressure of 800 kPa on
  the refrigerant. The refrigerant is now heated
  until its temperature is raised to 50OC.
  Calculate the work done during this process.

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• Initial state
• P1800kPa, saturated liquid
• v1vL_at_p1800kPa0.0008454 m3/kg From A-12
• Final state
• P2200kPa, T250OC (Superheated)
• v2 0.02846 m3/kg From A-13

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• Problem 6 A mass of 1.2 kg of air at 150 kPa and
  12OC is contained in a gas-tight, frictionless
  piston-cylinder device. The air is now compressed
  to a final pressure of 600 kPa. During the
  process, heat is transferred from the air such
  that the temperature inside the cylinder remains
  constant. Calculate the work input during this
  process.
• Temperature is constant through out the process

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• Problem 7 Nitrogen at an initial state of 300K,
  150 kPa and 0.2 m3 is compressed slowly in an
  isothermal process to a final pressure of 800
  kPa. Determine the work done during this process.
• Isothermal Process

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• Problem 8 A gas is compressed from an initial
  volume of 0.42m3 to a final volume of 0.12m3.
  During the quasi-equilibrium process, the
  pressure changes with volume according to the
  relation , where a-1200kPa/m3 and b600kPa.
  Calculate the work done during this process (a)
  by plotting the process on a P-V diagram and
  finding the area under the process curve and (b)
  by performing the necessary integrations.

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a) Area of process on P-v diagram is a Trapezoidal
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b) Work done by Integration
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• Problem 9 During some actual expansion and
  compression processes in piston-cylinder devices,
  the gases have been observed to satisfy the
  relationship PVnC, where n and C are constants.
  Calculate the work done when a gas expands from a
  state of 150 kPa and 0.03m3 to a final volume of
  0.2m3 for the case of n 1.3.
• The process is polytropic n1.3
• P1150 kPa, V10.03m3
• V2 0.2m3, P2?

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• Problem 11 Determine the work required to
  accelerate a 2000kg care from 20 to 70 km/h on an
  uphill road with a vertical rise of 40m.
• The work done body is the sum change in kinetic
  energy and potential energy of the body.
• m2000kg, v120km/h, v270km/h, z240m

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• Problem 13
• Determine the work required to deflect a linear
  spring with a spring constant 70kN/m by 20 cm
  from its position at rest.
• Given k70kN/m, x10 and x220cm0.2m

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• Problem 14
• Determine the power required for a 2000kg car to
  climb a 100m long uphill road with a slope of 30O
  (from horizontal) in 10s (a) at a constant
  velocity, (b) from rest to a final velocity of 30
  m/s, and (c) from 35 m/s to a final velocity of 5
  m/s. Disregard friction, air drag and rolling
  resistance.
• Solution
• M2000kg, z2100m, z10
• Work done Wtotal Wa Wg

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• Problem 12
• Refrigerant 134a enters the compressor of a
  refrigeration system as saturated vapor at 0.14
  MPa, and leaves as superheated vapor at 0.8 MPa
  and 50OC at a rate of 0.04kg/s. Determine the
  rates of energy transfers by mass into and out of
  the compressor. Assume the kinetic and potential
  energies to be negligible.
• Solution
• Inletof comprssorP10.14MPa, saturated vapor
• h1hg_at_p10.14MPa236.04kJ/kg From A-12
• Outlet of compressor P20.14, T250OC,
  Superheated h2284.36kJ/kg From A-13

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• Problem 15
• A mass of 5 kg of saturated liquid-vapor mixture
  of water is contained in a piston cylinder device
  at 100 kPa. Initially, 2kg of the water is in the
  liquid phase and the rest is in the vapor phase.
  Heat is now transferred to the water, and the
  piston, which is resting on a set of stops,
  starts moving when the pressure inside reaches
  200kPa. Heat transfer continues until the total
  volume increases by 20 percent. Determine (a) the
  initial and final temperatures, (b) the mass of
  liquid water when the piston first starts moving,
  and (c) the work done during this process. Also,
  show the process on a P-v diagram.Initial state.
• Solution
• P1100kPa, saturated Mixture
• T1Tsat_at_P1100kPa99.63OC From A-5
• V1mfvfmgvg2x0.0010443x1.67295.02m3

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Final state P3200kPa, vapor phase