Rinkel's modification of Ruchhardt's method

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In summary, Homework Equations Rinkel's modified experiment: - A ball of mass is placed in a tube connected to a container of gas with pressure slightly greater than atmospheric pressure.- The ball undergoes simple harmonic motion with a period given by 2 pi sqrt(frac{mV}{gamma p A^2}).- In Rinkel's modified experiment, the ball is held in a position where the gas pressure in the container is equal to air pressure. Then it is let go and the distance it falls before starting to go up is measured.- This distance is given by mgL = gamma pA2 L2/2V.
  • #1
arpon
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Homework Statement


upload_2015-6-4_10-38-43.png

In Ruchhardt’s method of measuring ##\gamma##, illustrated in Fig. 12.2, a ball of mass ##m## is placed snugly inside a tube (cross-sectional area ##A##) connected to a container of gas (volume ##V##). The pressure ##p## of the gas inside the container is slightly greater than atmospheric pressure ##p_0## because of the downward force of the ball, so that
##p = p_0 + \frac{mg}{A}##
Show that if the ball is given a slight downwards displacement, it will undergo simple harmonic motion with period ##T## given by
##T = 2\pi \sqrt{\frac{mV}{\gamma p A^2}}##
[You may neglect friction. As the oscillations are fairly rapid, the changes in ##p## and ##V## which occur can be treated as occurring adiabatically.]
In Rinkel’s 1929 modification of this experiment, the ball is held in position in the neck where the gas pressure ##p## in the container is exactly equal to air pressure, and then let drop, the distance ##L## that it falls before it starts to go up again is measured.
Show that this distance is given by
##mgL = \frac{\gamma pA^2 L^2}{2V}##

Homework Equations


##pv^\gamma = const. ##

The Attempt at a Solution


I have correctly derived the first equation of period of the SHM.
From this equation, I got,
##\omega ^2 = \frac{pA^2\gamma}{mV}##
upload_2015-6-4_10-54-49.png

As the initial velocity is 0, so
## L = 2 \cdot amplitude##
Applying energy conservation for the point A & B, we get:
##mgL = \frac{1}{2} m \omega^2 (\frac{L}{2})^2##
##mgL = \frac{pA^2 \gamma L^2}{8V}##
 
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  • #2
Hi arpon. You got so involved with presenting this that you forgot to add your question?
 
  • #3
NascentOxygen said:
Hi arpon. You got so involved with presenting this that you forgot to add your question?
Here is the question:
arpon said:
Show that this distance is given by
##mgL = \frac{\gamma pA^2 L^2}{2V}##
 
  • #4
forum rules stipulate that complete solutions to homework problems are not allowed
In the second part, I am afraid your application of energy conservation is not accurate; since in both points A and B you should be getting:
Kinetic energy = 0, Potential energy = ##\frac{1}{2} k A^2## for each of them, which do not give the expression required.

So, my approach would be to break down the different force mechanisms here:
There are 2 forces acting upon the ball: The downward gravitational force ##mg## and the upward excess pressure ##\Delta P## which is given by $$\Delta P = \gamma \frac{P_0}{V_0}\Delta V.$$
Here, ##P_0=p_0=p## is the pressure and ##V_0=V## is the volume at point A in the Rinkel's modification set up of the experiment. (Note that the above formula for excess pressure follows directly from the adiabatic nature of the whole process. Just take the derivative of ##PV^\gamma =## constant.)

[ mentor note: some content in this post has had to be edited out to make it compliant with PF homework help rules ]
 
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Related to Rinkel's modification of Ruchhardt's method

1. What is "Rinkel's modification of Ruchhardt's method"?

Rinkel's modification of Ruchhardt's method is a technique used in analytical chemistry for the determination of the concentration of a substance in a solution. It is a modification of Ruchhardt's method, which was developed in the late 1800s.

2. How does Rinkel's modification differ from Ruchhardt's method?

Rinkel's modification involves the use of a color indicator to determine the endpoint of the reaction, while Ruchhardt's method relies on titrating until a particular color change is observed. Additionally, Rinkel's modification uses a standardized solution for the titration, making it more precise and accurate.

3. What is the principle behind Rinkel's modification of Ruchhardt's method?

Rinkel's modification is based on the reaction between the substance being analyzed and a standard solution of potassium permanganate. The amount of potassium permanganate used in the titration is then used to calculate the concentration of the substance in the sample.

4. What types of substances can be analyzed using Rinkel's modification?

Rinkel's modification can be used to analyze a wide range of substances, including reducing agents, aldehydes, and sugars. It is commonly used in the analysis of food and beverages, as well as in environmental and industrial applications.

5. What are the advantages of using Rinkel's modification over other analytical methods?

Rinkel's modification is a simple, fast, and accurate method for determining the concentration of a substance in a solution. It also requires minimal equipment and can be easily performed in a laboratory setting. Additionally, it is less affected by interfering substances compared to other methods, making it a reliable choice for many applications.

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