Determining the Specific Heat Capacity of Air

Contents Ⅰ： Aim Ⅱ： Introduction Ⅲ： Theory Ⅳ： Experimental Process Ⅴ： Instruments and Data Table

Ⅰ： 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.

Ⅱ：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 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.

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:

Ideal gas relations Furthermore, the heat capacities can be expressed in terms of heat capacity ratio ( γ ) and the gas constant ( R ): and So：

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):

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

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

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).

Ⅲ：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 = 8.314472J·mol−1·K−1

Isentropic process (Reversible adiabatic process) Calculations Process Constant Equation Isobaric process Pressure V/T=constant Isochoric process Volume P/T=constant Isothermal process Temperature PV=constant Isentropic process (Reversible adiabatic process) Entropy PVγ=constant Pγ-1/Tγ=constant TVγ-1=constant

Isotherms of an ideal gas T: high T: low

Ⅳ: Experimental process Ⅰ(P1,T0) Ⅱ(P0,T1) Ⅲ(P2,T0) Adiabatic expansion Isochoric process (pressure increase)

Adiabatic expansion.Ⅰ(P1,T0)----Ⅱ(P0,T1) Calculations Adiabatic expansion.Ⅰ(P1,T0)----Ⅱ(P0,T1) Equation 1

Calculations Isochoric process (pressure increase). Ⅱ(P0,T1)------Ⅲ(P2,T0) Equation 2

Calculations Through equation 1 and 2 Equation 3

Ⅴ:Instruments and data table

Testing Instrument

Sensitivity The Pressure Sensor:20mV/kPa The Temperature Sensor:5mV/K

Data table P0（kPa） T0 ΔP1 (mV ) P1 (kPa) (mV) P2 （kPa） γ 1 101.30 2 3 4 5 6

Result