1. Determining the Specific Heat Capacity of Air

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

3. 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.

4. 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.

5. 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:

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

7. 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):

8. 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

9. 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

10. 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 (273.15 K) and pressure of  kPa (1 atm).

11. 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 =  J·mol−1·K−1

12. 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

13. Isotherms of an ideal gas
T: high
T: low

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

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

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

17. Calculations
Through equation 1 and 2
Equation 3

18. Ⅴ:Instruments and data table

19. Testing Instrument

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

21. Data table P0（kPa） T0 ΔP1 (mV ) P1 (kPa) (mV) P2 （kPa） γ 1 101.30 2 34 5 6

22. Result