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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 (C P ) to heat capacity at constant volume (C V ). It is sometimes also known as the isentropic expansion factor and is denoted by γ (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 ( γ ) and the gas constant ( R ): and So

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Relation with degrees of freedom The heat capacity ratio ( γ ) 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 (N 2 ) and ~21% oxygen (O 2 )) 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 GasRatio of Specific Heats Carbon Dioxide1.3 Helium1.66 Hydrogen1.41 Methane or Natural Gas1.31 Nitrogen1.4 Oxygen1.4 Standard Air1.4

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One Standard Atmosphere Common Pressure Units frequently used as alternative to "one Atmosphere" 76 Centimeters (760 mm) of Mercury Meters of Water 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 ( K) and pressure of 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 = J·mol 1 ·K 1

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Calculations ProcessConstantEquation Isobaric processPressureV/T=constant Isochoric processVolumeP/T=constant Isothermal process TemperaturePV=constant Isentropic process (Reversible adiabatic process) Entropy PV γ =constant P γ-1 /T γ =constant TV γ-1 =constant

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Isotherms of an ideal gas T: high T: low

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: Experimental process (P 1,T 0 ) (P 0,T 1 ) (P 2,T 0 ) Adiabatic expansion Isochoric process (pressure increase)

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Calculations Adiabatic expansion. (P 1,T 0 )---- (P 0,T 1 ) Equation 1

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Calculations Isochoric process (pressure increase). (P 0,T 1 ) (P 2,T 0 ) 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 Sensor:20mV/kP a The Temperature Sensor:5mV/K

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Data table P 0 kP a T0T0 ΔP 1 (mV ) P 1 (kP a ) ΔP 1 (mV) P 2 kP a γ

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Result

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