Determining Minimum Waiting Time for an Alcohol Thermometer

Thermodynamics Experiment 1: Temperature Measurement

March 28, 2016

A very basic experiment, we conducted this experiment to find the minimum waiting time before a thermometer displays an accurate temperature measurement. Generally, the thermometer measures the heat transfer between the object and the thermometer. For an alcohol thermometer, the alcohol inside the glass expand linearly as the temperature increases. 

In theory, for a linear temperature sensor, the rate of change of ΔT=Tf - Ti is directly proportional to the decreasing ΔT. That is,

dΔT/dt = -kΔT,

(1)

      where k must be 1/𝝉, and 𝝉 is the minimum waiting time. This is a pretty straightforward derivation using rate of change. Integrating both sides, we will get the simple equation,

T(t) = Ti + ΔT(1-e^(-t/𝝉))

(2)

The experiment was divided into two parts: heating and cooling. In heating, the final temperature Tf was the temperature of the hot bath and the initial temperature Ti was recorded from the cup of ice. T(𝝉), and succeding time constants, were computed beforehand. The time it took for the temperature change from Ti to T(𝝉), T(2𝝉), T(3𝝉), ... were recorded. The same procedure were implemented for the cooling part except that Tf is the temperature in cup of ice, and Ti the temperature on the hot bath.

Using Equation 2, we linearize the time recorded and get the inverse of the slope to obtain the time constant 𝝉.

Figure 1. Sample linearized plot of t vs t/𝝉.

The average 𝝉 obtained is 6.29 for the heating part and 11.39 for the cooling part (not including the outlying values). The total average time constant is 8.84, and it is accepted to wait 3 to 5 time constants

(~30 sec to 2 min). However, the system being observed on the experiment was water. For a real fever, Tf will increase, thus, increasing time for stabilization. And this will lead to a minimum waiting time of at least three and a half minutes[1].


Footnote(s):
1. Huber, Mike, Teaching Differential Equations with Modeling and Visualization- Fever, August 2010. Retrieved from <<http://www.codee.org/library/projects/teaching-differential-equations-with-modeling-and-visualization>>.

Verifying Snell's Law on Optical Disks

Experiment 6: Optical Disk – Reflection and Refraction 

January 25, 2016

As I learned during my high school physics, light, as it travels through a medium, is either reflected or refracted. This is because the speed of light varies for each medium. The most common
\[\begin{equation}
c = 3 x 10^8 m/s\label{a}\tag{1}
\end{equation}\]
is the speed of light in vacuum. For other medium, the speed of light is related by the refractive index n given by
\[\begin{equation}
n = \frac cv\label{b}\tag{2}
\end{equation}\]
where v is the speed of light on that medium. This will determine if the light will either be reflected or refracted, as shown in Figure 1.

Figure 1. An incident light strikes a surface with two different media.

< Image from: Lab Manual Authors, Physics 73.1 Laboratory Manual, 2013>

Figure 2. Diagram of the experiment.

Figure 2 shows a diagram of the experiment conducted. The different media are placed on the optical disk. These include mirrors (plane, convex, and concave), glasses (semicircular, triangular, trapezoidal) and lenses (double convex, double concave). 

The law of reflection was observed on all kind mirrors. That is, referring from Figure 1, the angle of the incident ray (θ1) is equal to the angle of the reflected ray (θ1'). This was because the incident ray is striking normal to the surface of the mirror, even if it is not plane, as long as the mirror stays on the center of 90°-90° axis of the optical disk. Any offset on its placement will not result to the law of reflection.

Figure 3. Reflection from a concave mirror at 0°.

Figure 4. Reflection from a plane mirror at 10°.

As for the semicircular glass, a reflected part and a refracted part is observed. The light as it strikes the center of semicircular glass (both on the plane part and on the curved part), reflects at the same angle the incident ray was striking. However a critical angle of 43.75° was observed, hence there was no reflected light observed when the incident ray strikes at 50°. 

The refraction was taking place inside the glass. The point when the light passes from the glass to the air again exhibits no reflection and refraction. Hence, there is a total internal reflection.

The average index of refraction observed is equal to 1.48. Using Equation 2 to find the speed of light inside the glass is found to be equal to 2.03 E +08 m/s.

For the other glass shapes, the following refraction are observed:

Figure 5. Refraction in a double concave lens.

Figure 6. Refraction in a double convex lens.

Figure 7. Refraction in a triangular glass through the shorter side.

Figure 8. Refraction in a triangular glass through the longer side.

Figure 9. Refraction in a trapezoidal glass through the shorter base.

I therefore conclude, that every mirror exhibit reflection. Furthermore, as light passes through a medium, it travels slower than the speed of light in vacuum, producing refractive index greater than 1.

* Figures 3 to 9, All images taken by Karlo de Leon, January 25, 2016.

Introduction

This blog is made by

REINIER XANDER A. RAMOS

A BS Applied Physics student from the
National Institute of Physics
College of Science
University of the Philippines
Diliman, Quezon City

In Partial Fulfillment of the Requirements
For the Course of
Physics 103.1: Fundamental Physics Lab III

January 2016