Determining the Specific Heat Capacity of Air

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Determining the Specific Heat Capacity of Air
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Contents
? Aim ? Introduction ? Theory ? Experimental
Process ? Instruments and Data Table
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? Aim

• To measure the specific heat ratio of air by the
  method of adiabatic expansion.
• To learn how to use the temperature sensor and
  the pressure sensor.

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?Introduction

• The heat capacity ratio or adiabatic index or
  ratio of specific heats, is the ratio of the heat
  capacity at constant pressure (CP) to heat
  capacity at constant volume (CV). It is sometimes
  also known as the isentropic expansion factor and
  is denoted by ? (gamma).
• where, C is the heat capacity or the specific
  heat capacity of a gas, suffix P and V refer to
  constant pressure and constant volume conditions
  respectively.

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Ideal gas relations

• For an ideal gas, the heat capacity is constant
  with temperature. Accordingly we can express the
  enthalpy as H CPT and the internal energy as U
  CVT. Thus, it can also be said that the heat
  capacity ratio is the ratio between the enthalpy
  to the internal energy

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Ideal gas relations

• Furthermore, the heat capacities can be expressed
  in terms of heat capacity ratio ( ? ) and the gas
  constant ( R )
• and
• So

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Relation with degrees of freedom

• The heat capacity ratio ( ? ) for an ideal gas
  can be related to the degrees of freedom ( f ) of
  a molecule by
• Thus we observe that for a monatomic gas, with
  three degrees of freedom
• while for a diatomic gas, with five degrees of
  freedom (at room temperature)

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E.g.

• The terrestrial air is primarily made up of
  diatomic gasses (78 nitrogen (N2) and 21
  oxygen (O2)) and, at standard conditions it can
  be considered to be an ideal gas. A diatomic
  molecule has five degrees of freedom (three
  translational and two rotational degrees of
  freedom). This results in a value of

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Ratio of Specific Heats for some common gases
Gas Ratio of Specific Heats
Carbon Dioxide 1.3
Helium 1.66
Hydrogen 1.41
Methane or Natural Gas 1.31
Nitrogen 1.4
Oxygen 1.4
Standard Air 1.4
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One Standard Atmosphere

• Common Pressure Units frequently used as
  alternative to "one Atmosphere"
• 76 Centimeters (760 mm) of Mercury
• 10.332 Meters of Water
• 101.33 Kilopascal
• Note Standard atmosphere is a pressure defined
  as 101'325 Pa and used as unit of pressure
  (symbol atm).
• The original definition of Standard
  Temperature and Pressure (STP) was a reference
  temperature of 0 C (273.15 K) and pressure of
  101.325 kPa (1 atm).

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?Theory

• Ideal gas law
• The state of an amount of gas is determined by
  its pressure, volume, and temperature according
  to the equation
• where
• P is the absolute pressure of the gas,
• V is the volume of the gas,
• n is the number of moles of gas,
• R is the universal gas constant,
• T is the absolute temperature.
• The value of the ideal gas constant, R, is found
  to be as follows.
• R  8.314472Jmol-1K-1

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Calculations
Process Constant Equation
Isobaric process Pressure V/Tconstant
Isochoric process Volume P/Tconstant
Isothermal process Temperature PVconstant
Isentropic process (Reversible adiabatic process) Entropy PV?constant P?-1/T?constant TV?-1constant
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Isotherms of an ideal gas
T high
T low
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? Experimental process
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Calculations
Adiabatic expansion.?(P1,T0)----?(P0,T1)
Equation 1
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Calculations

• Isochoric process (pressure increase).
• ?(P0,T1)------?(P2,T0)

Equation 2
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Calculations

• Through equation 1 and 2

Equation 3
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?Instruments and data table
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Testing Instrument
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Sensitivity

• The Pressure Sensor20mV/kPa
• The Temperature Sensor5mV/K

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Data table
P0(kPa) T0 ?P1 (mV ) P1 (kPa) ?P1 (mV) P2 (kPa) ?
1 101.30
2 101.30
3 101.30
4 101.30
5 101.30
6 101.30
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Result