ENGR 260 Sections 4'34'4

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ENGR 260Sections 4.3-4.4
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Specific Heats

• Specific Heat the energy required to raise
  temperature of one unit mass one degree
  (kJ/kgºC)
• The amount of energy depends on how this process
  is executed. It is path dependent.

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Two kinds of specific heat of interest

• Specific heat at constant volume cv
• Specific heat at constant pressure cp
• Which is higher cv or cp for a substance?
• Cp is always higher because it allows for
  expansion which must include boundary work.

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Energy Balance for a stationary closed system
The change in internal energy with temperature at
constant volume.
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Similarly a constant pressure expansion yields
The change in enthalpy with temperature at
constant pressure.
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Temperature Dependent

• Both cv and cp are dependent on temperature since
  internal energy and enthalpy are dependent on
  temperature.

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Example 1

• Find the specific heat of air for a constant
  pressure process at 27C.
• Find the specific heat of CO2 for a constant
  pressure process at 500K.
• Find the specific heat of N2 for a constant
  pressure process at 357C.

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Constant pressure specific heats for some ideal
gases. (kJ / kmolK)
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The big picture?

• What is specific heat?
• How might I use it?

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Ideal Gases(Enthalpy Internal Energy
Relationship)
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Ideal Gases(Enthalpy Internal Energy)
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Estimations of Internal Energy and Enthalpy for
Ideal Gases
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Specifics Heats of Ideal Gases
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Determining Ideal Gas Internal Energy Enthalpy

• 1) Use tabulated u and h data.
• Easiest
• Most accurate
• Use cv or cp relations to temperature and perform
  the integrations
• Inconvenient for hand calculations
• Convenient for computerized calculations
• Very accurate
• Use average specific heats
• Simple and convenient
• Reasonable accurate for small temperature
  intervals

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Specific Heat RelationsOf Ideal Gases
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Specific Heat Ratio

• For monatomic gases k1.667
• For diatomic gases k1.4

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Example

• A piston cylinder device initially contains 0.5
  m3 of nitrogen gas at 400 kPa and 27oC. An
  electric heater within the device is turned on
  and is allowed to pass a current of 2 A for 5
  minutes from a 120 V source. Nitrogen expands at
  constant pressure, and a heat loss of 2800 J
  occurs during the process. Determine the final
  temperature of nitrogen.

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Example

• A piston cylinder device initially contains air
  at 150 kPa and 27oC. At this state, the piston
  is resting on a pair of stops, and the enclosed
  volume is 400 L. The mass of the piston is such
  that a 350 kPa pressure is required to move it.
  The air is now heated until its volume has
  doubled. Determine (a) the final temperature,
  (b) the work done by the air and (c) the total
  heat transferred to the air.