Introduction
Substances vary from one another in the amount of heat needed to produce a rise in temperature in a given quantity of gas. The quantity of heat needed to change the temperature of a system is proportional to the mass of that system as well as the change of temperature. This is expressed as where Q is the amount of heat required, m is the mass of the system, c is the specific heat, and is a change in temperature. The values of specific heat depend on some extend of temperature. In small temperatures, the specific heat is considered as a constant. Also, the specific heat depends on the type of processes heating. Sometimes a process is assumed to have carried on in a constant pressure-atmospheric pressure denoted as cp. If the volume of the system is kept constant, the specific heat is referred to as “specific heat at constant volume” denoted as cv. both cp and cv are assumed to be equal.
..1
The difference between cp and cv of gases between are different explained in terms of first la w of thermodynamics as well as the kinetic theory of gases. The molar heat capacity at constant volume is introduced as and molar heat capacity at constant pressure as that are referred to as the heat needed to raise one mole of a gas by one kelvin at a constant volume at a constant pressure. Change in internal energy of an ideal gas is expressed as where Cv is molar capacity of heat of the gas at a constant volume, n is mole number, and is the change in temperature between the gas states.
An ideal gas undergoes a quasi-static process in the relationship. When a gas undergoes adiabatic decompression from state S1(PI,V1,T1) at room temperature to another state S0(P0,V0,T0) where T0<T1 and P0 = atmospheric pressure, then followed by isochoric heating to another state S2(P2,V2,T2) where temperature returns to the initial temperature, that is, T2=T1. This can be shown as below:
2
A manometer can be used to determine the relative height of columns h1 and h2 that are associated with pressure variations between P1 and P0, P2 and P0 respectively. In Ruchhardt method, a syringe with a piston is used, the period T of oscillations measured. With mass, m and cross-sectional area of the piston, a differential equation for the simple harmonic motion can be formulated: . Here, y is the piston displacement. Solving for , the equation becomes,. Then becomes. P is the total pressure enclosed air plus the weight of the piston, that is, .
Aims and Objectives
The purporse of this experiment is to determine the of the air using two different methods, that is Clément and Désormes’ method and Rüchhardt’s method.
Apparatus
Flask cap
Drying tubing
A manometer
6 liter glass flask
Rubber blunder
Thermometer
A tygon tubing
A tube connector
Two pitching clamp
Drying agent
Syringe
Piezostrip
Barometer;
An Oscilloscope;
A Caliper;
A Scale;
A Printer;
A Lab stands;
Cables.
Procedure
The first step of the method was to get familiar with the equipment: a check on the manometer was done to be sure that the connections and operations were well understood. The oscilloscope and the piezostrip were checked to understand the connections, settings, controls and the operations. The cables and tubing connections of the setup were checked as well.
A Clément and Désormes’ method
Figure 1. Clément and Désormes’ method
The setup in the above figure was confirmed; the paraffin oil in the two arms of the manometer was confirmed to be at the same level.
The below process was repeated five times: With a tygon pitching clamp open, the glass flask was filled with air using the bladder to obtain a higher pressure than the atmospheric pressure, that is, (P1>P0). The flask was allowed to settle at room temperature and the height difference, h1, between the two arms was taken. The room temperature was taken. With the bladder disengaged, the pinching clamp was unscrewed quickly to enable the air in the flask to return to atmospheric pressure. The [inching clamp was closed again. An increase in temperature after return of pressure to P0 was observed, the height difference between the two arms, h2 and temperature T2 were recorded.
B. Rüchhardt’ method
The setup in figure 2 was confirmed. The diameter and the weight of the piston were measured using a caliper and scale respectively. The oscilloscope was set to read a single trigger at a time. The piezostrip was brushed and set to observe the waveform. Atmospheric pressure measurements were taken.
The below process was repeated five times: the syringe was filled with 30 ml of air and the actual volume taken. The piston was depressed to a reasonable depth increasing the pressure in the syringe. The pressure on the piston was released to allow the syringe to oscillate. The oscillations were displayed on the oscilloscope and a printout generated.
Figure 2. Rüchhardt’ method
Results
Figure 3 a) Figure 3 b)
Figure 3 c) Figure 3 d)
Figure 3 e).
The data below shows the results of the first experiment
T1=22.0 C T2=22.5 C
P1=73.67 mmHg P2=73.67mmHg
L1 = 61.4 cm +/- 0.05 cm
H1 = 80. 7 cm
H2 = 63.6 cm
H1 = 79. 6 cm
H2 = 63.4 cm
H1 = 81.0 cm
H2 = 63.4 cm
H1 = 76.7 cm
H2 = 63.3 cm
H1 70.5 cm
H2 62.6 cm
Volumes
V1 = 24. 5 ml
V2 = 22. 0 ml
V3 = 19.5 ml
V4 = 22.5.0 ml
V5 = 24.0 ml
Average heights
H1=
H2=
Average volume =
Average mass
M1 =
M2 =
Average mass =
Questions and answers
Questions and answers
Why is the drying agent necessary? How the results would change if it was not used;
Answer: to evict any possibility of moisture in the expeiment.
Why time is critical for the Clément-Désormes method to work?
Answer: time is a factor in the experiment. A short time is required for the temperature to rise to room temperature.
How can the natural frequency of the piezostrip interfere with the results?
Answer: unwanted oscillations will occur at the end of the experiment.
Discussions
Classical measurement of the ratio of specific heats of air is a superb experiment in an introductory laboratory in thermodynamics. Both Clément’s and Ruchhardt are excellent methods that confirm this factor. In this experiment, the Clément’s method employed the use of a small mass of air undertaken to adiabatic expansion and then isochoric process to return to the initial temperature. However, Clément’s method is not recommended: first, relatively large amount of air is confined at a higher pressure than the atmospheric pressure; second, difficulties in measurement of exact pressures make it an inaccurate method. Ruchhardt method comes to perfect the incapability of the Clement’s method. Here, the effect can be monitored in a digital oscilloscope. The values are valid and computation is easier.
Conclusion
Using the Clément’s and ruchhardt method to measure the ratio of specific heat in air has a varied accuracy. The Ruchhardt is more modern compared to the latter; a digital application of an oscilloscope makes it a better method of estimating the ratio.
Work cited
Burba, G, D Anderson, and G Burba. A Brief Practical Guide to Eddy Covariance Flux Measurements: Principles and Workflow Examples for Scientific and Industrial Applications. Lincoln, Neb: LI-COR, 2010. Print.
Chang, Hasok. Inventing Temperature: Measurement and Scientific Progress. Oxford: Oxford University Press, 2004. Print.
Foster, Clement L. N, and J S. Haldane. Investigation of Mine Air: An Account by Several Authors of the Nature, Significance, and Practical Methods of Measurement of the Impurities Met with in the Air of Collieries and Metalliferous Mines. London: C. Griffin & Co, 1905. Print.
