Laboratory work #4
Definition of the rate of adiabat

Aim of the work: Investigation of the isoprocesses of ideal gas.

Tasks: 1) To learn the Kleman – Dezorm method; 2) To determine the rate of adiabat for air using the Kleman – Dezorm method.

Experiment

To define the adiabat of the air [pic] in this work it is used the classical Kleman – Dezorm method. Initially, the system (gas) is in state 1, which is characterized by thermodynamic parameters: temperature T1, pressure p1 and specific volume v1 (volume of unit of mass of gas). Making the adiabatic expansion process gas transfers to the state 2 (fig. 1) with parameters Т2,р2,v2. Then the system is heated at the constant volume v2 till the temperature T3, which is equal to initial temperature T1, that is in final state parameters are equal to Т3,р3,v3. (Т3=Т1, v3 = v1). As the process 1-2 is adiabatic, then

[pic] (1)

where γ is rate of adiabat for given gas. In state 1 and 3 gas has the same temperature (isothermal process), applying the Boyle – Mariotte low, get

[pic] (2)

[pic] Figure 1 Figure 2

From given equations (1) and (2) it is simply to get

[pic] (3)

Therefore the rate of adiabat γ is defined:

[pic] (4)

Usually the experiment is carried out such way, that p2 is equal to atmospheric, barometric pressure. Then the pressure in states 1 and 3 could be express thought p2

[pic] (5)

where h1 and h3 are readings of manometer in graduations of its scale; [pic] is density of liquid in manometer. Considering (5) equation (4) could be present as:

[pic] (6) Considering that [pic] and using the approximate equation [pic] at [pic]we can get the equation for definition of the rate of adiabat

[pic].

Thus, the rate of adiabat [pic]for air can be defined according equation (7) by the Kleman – Dezorm method of adiabatic state of the gas.

Experimental device

Experimental device (fig.2) for definition of the rate of adiabat by the Kleman – Dezorm method consists of big glass balloon 1, connected through tap 2 with pump, with the help of which air is pumped to the balloon at the open tap. For measurement of excess pressure it is used U-shape manometer 3. For blowing-off the air from the balloon and connection of it with the atmosphere it is used more one tap 4.

Experiment holding

1. At the closed balloon (the tap 4 is close) and the opened tap 2 the air is pumped to the balloon till the difference of liquid levels in manometer get 300-350 graduations (mm).
2. Close tap 2 and wait 3-5 minutes till the temperature in the balloon matches with the environment temperature and the pressure is established finally, make the indication of h1 of the difference of liquids levels in manometer.
3. Quickly open the tap 4 on the short time and close after stopping of sizzle of going out air, that is correspond of pressure alignment inside of balloon with atmosphere pressure.
4. Wait 3-5 minutes, when the air in the balloon is heated till the environment temperature, make the second indication of the difference of liquids levels in manometer h3.
5. Make the experiment 3-5- times, changing magnitude h1.
6. Results of the measurements put into the table 1.

Table 1
|Test |h1 |h3 |( | |(( |(=((( |(,% |
|№ | | | | | | | |
| | | | | | | | |

Data Analysis

1. Calculate according to the equation (7) the rate of adiabat ( for air [pic] (7) 2. Estimate the absolute and relative errors of measurements according to the method of small-sample statistics for Р=0.95. 3. Results of the measurements put into the table 1.. 4. The obtained result compare with the theoretical value of (, calculated through the number of degrees of freedom. Estimate the possible sources of errors of this method. 5. Analyze the obtained results and formulate the conclusions.