Experiment 3. Temperature Measurement

Experiment 3.  Temperature Measurement



The objectives of the experiment are the following:

- to measure thermal time constants of different temperature sensors
- to determine minimum waiting time before reading measurements of temperature
- characterize response of different thermal sensors with temperature

Introduction

Thermal equilibrium is the state wherein no more changes in the warmness or coldness occur when two objects, one warm and one cold are placed in contact with each other. Temperature is the quantity which is the same for the two bodies that are in contact and in thermal equilibrium.

The time constant is the time it takes for a temperature sensor to have a reading equal to its initial reading plus 0.632 times the difference between its initial and final reading.

T(t=z) = Ti + 0.632 (Tf-Ti)  (1)

It can be used to specify how long one must wait to get a reliable temperature reading. It is common engineering practice to wait for three to five time constants before reading the output of a thermometer. A material with a linear thermometric property has identical responses to heating and cooling - its cooling and heating time constants are the same.

In measuring temperature, we measure the degree of change in the properties of a material to heat and cold. In this experiment, three temperature sensors were used and studied: alcohol thermometer, mercury thermometer and a thermocouple.


Methodology

The experiment is divided into two parts for each of the three temperature sensors: the heating procedure and the cooling procedure.

Heating Procedure

A pot was filled with water up to 3/4 of its size. The water was kept boiling throughout the activity. The thermometer was dipped into the hot water. When the temperature stopped increasing, the final temperature Tf was recorded. The thermometer was then dipped on ice water. When the temperature reading stopped decreasing, the temperature was recorded as Ti.
Value for T(z) was computed and tabulated.
With the initial temperature Ti, the thermometer was dipped in boiling water and the time it took for the reading to reach T(z) was recorded.

Cooling Procedure
A pot was filled with water up to 3/4 of its size. The water was kept boiling throughout the activity. The thermometer was dipped on ice water. The final temperature, Tf, was recorded. The thermometer was dipped on boiling water until its temperature stopped increasing. The initial temperature Ti was recorded on the worksheet. Values for T(z) was computed. Initially with temperature Ti, the thermometer was dipped on ice water and the time it took for the reading to reach each T(z) was calculated. These values were recorded.

Results and Discussion

The following data were gathered:

Table W1. Alcohol thermometer

(  a)    Heating

Trial	Tf (°C)	Ti (°C)	T(z) (°C)	z(s)
1	95	1.0	60.408	6.0
2	95	1.0	60.408	5.8
3	95	1.5	60.592	5.7
Average				5.83

(b)   Cooling

Trial	Tf (°C)	Ti (°C)	T(z) (°C)	z(s)
1	2.0	94	35.9	5.8
2	0	94	34.6	6.2
3	0	94	34.6	6.0
Average				6.0

Table W2. Mercury thermometer

(a)    Heating

Trial	Tf (°C)	Ti (°C)	T(z) (°C)	z(s)
1	100	3.0	64.3	2.3
2	100	4.0	64.7	1.9
3	100	4.0	64.672	2.0
Average				2.07

(a)    Cooling

Trial	Tf (°C)	Ti (°C)	T(z) (°C)	z(s)
1	1.0	100	37.432	1.8
2	2.0	100	38.064	2.12
3	3.0	100	38.696	2.0
Average				1.9733

Table W3. Thermocouple

(b)   Heating

Trial	Tf (°C)	Ti (°C)	T(z) (°C)	z(s)
1	96.5	1.70	61.6136	0.3
2	96.5	1.70	61.6136	0.3
3	96.5	1.70	61.6136	0.3
Average				0.3

(b)   Cooling

Trial	Tf (°C)	Ti (°C)	T(z) (°C)	z(s)
1	96	-2.0	34.1	0.2
2	96	-2.0	34.1	0.2
3	96	-2.0	34.1	0.2
Average				0.2

It was shown that the thermocouple had the lowest values of time constant among the three, with a time constant of 0.3 for heating and 0. 2 for cooling. Among the three, it responses the fastest for during changes in temperature. The thermocouple is more linear with close time constants of 0.3 and 0.2 for heating and cooling, respectively.

Summary

The thermometric sensor that registered the fastest response to changes in temperature is the thermocouple, followed by the mercury thermometer and the slowest was the alcohol thermometer.

Experiment 2: Interference and Diffraction

The main goals of the experiment are to:
* investigate patterns produced by single-slit diffraction and double-slit diffraction
* quantitatively relate the single-slit diffraction pattern to the slit width size
* quantitatively relate the double-slit diffraction pattern to the slit width size
* quantitatively relate slit separation pattern and double-slit diffraction pattern

The materials used were the following:

* Laser diode
* Optical bench
* Single slit disk
* Multiple slit disk
* White paper screen
* Pencil
* Ruler
* Desk lamp

The first part of the experiment involved single-slit diffraction. We placed the laser at one end of the optics, and the single slit disk with its holder about 3 cm in from of the laser. The white sheet of paper was also placed away from the laser assuring that the laser would hit it. The 0.04 mm width single slit was selected. It was made sure that the slit and the pattern are of the same level vertically. The horizontal distance from the slit disk and to the screen was determined. The boundaries of the mth intensity minimum (located at the center of a dark fringe was marked. The length of the minima divided by two. This figure was considered as y1 in the table below. The same procedures were repeated using a slit width of 0.02 mm.

The following results were gathered:

Hence, it was clearly showed that the relationship a=mXL/y was validated where X=wavelength of light used.

Below are photos for the diffraction patterns for single slit, 0.04 mm and 0.02 mm, respectively.

As shown in the photos, the lower slit width value produced a longer central minimum.

The second part involved the double slit interference.

The same procedures for setting-up the optics materials was done. This time a double slit was used with distance separation of 0.25 mm and slit width of 0.04 mm. The following results were gathered.

In double slit interference, one can see a single-slit diffraction pattern which outlines how the fringes are grouped. The fringes are not of equal brightness and the intensity peaks are contained in the single-slit diffraction envelope.

It was also showed from the data that the relationship d=mXL/y was validated where X=wavelength of light used, L=horizontal distance from slit to the screen.

Diffraction pattern for double-slit interference

The third part was changing the slit width and slit separation in double-slit interference.

The following results were gathered.

In double slit interference, the width of interference fringes are controlled by the slit separation d. The diffraction envelope is controlled by the slit width a. Higher a = lower number of fringes and lower value for width of central maximum.Higher d, same a = higher value for width of central maximum.

These are the photos for Table W3.

A=0.08mm D=0.25mm

A=0.08mm D=0.50mm

A=0.04mm D=0.25mm

A=0.04mm D=0.50mm

References:

(1) Young, H. D., Freedman, R. A., Ford, A. L., & Sears, F. W. (2004). Sears and Zemansky's university physics: With modern physics. San Francisco: Pearson Addison Wesley.

Experiment 1

Experiment 1: Reflection and Refraction

The main goals of the experiment are the following:

·        -to investigate reflection and refraction of light using an optical disk

·        -to validate the Law of reflection and Snell’s law

·       - to trace the path of light as it emerges from optical materials of different geometries

          The first part of the experiment was the alignment of optics wherein the light source, the optical disk, the slit mask, the parallel ray lens are mounted on the optical bench. The parallel ray lens was placed between the slit plate and the optical disk. The slit mask was placed between the parallel ray lens and the optical disk. The optical components were adjusted to make the single ray coincident with the 0-0 axis of the optical disk. 

After the alignment of optics was the investigation of reflection by plane and spherical mirrors. The plane mirror was placed on the disk so that it coincided with the 90-90 angle axis or the component axis of the optical disk. It was made sure that the incident ray striked the center of the disk/mirror or the 0-0 axis of the disk. The optical disk was rotated such that the incident ray striked the center of the mirror at different angles of incidence. The same steps were repeated for both convex and concave mirrors.

The following results were gathered:

Table W1. Reflection by plane and spherical mirrors

Angle of incidence	Angle of reflection
	Plane mirror	Convex mirror	Concave mirror
10	10	10	10
20	20	20	20
30	30	30	30

This experiment on these three kinds of mirrors validated the law of reflection. The law states that the angle of reflection is equal to the angle of incidence for all wavelengths and for any pair of materials. 

The next part of the experiment still involved the three mirrors used. This time, the single slit was adjusted so that two or more rays served as incident rays on the mirror surface. The path of the incident rays were drawn after being reflected by the mirror.

The diagrams for the path of light are the following:

            In the plane mirror, light rays are parallel. In concave, light rays converge at a focus point while in convex mirror, light rays diverge from a focal point.

The third part is the reflection and refraction in glass.

The alignment of optics was performed. The mirror was replaced with a semicircular glass (cylindrical lens). The flat surface of the glass coincided with the component axis of the optical disk. The incident ray, reflected ray and the refracted rays coincided with the 0-0 axis.

The optical disk was rotated such that the incident ray is at 10 degree angle from the normal. The angles of reflection and refraction were obtained in increments of 10 degrees. The index of refraction was also calculated.

The results are the following:

Table W2. Reflection and refraction in glass with incident ray striking the flat surface

Angle of incidence	Angle of reflection	Angle of refraction	Index of refraction
10°	10°	7°	1.424871693
20°	20°	13.5°	1.465097176
30°	30°	19.5°	1.497872156
40°	40°	25.5°	1.493080235
50°	50°	31°	1.487354975
			Ave=1.473655247

                The index of refraction was calculated using Snell’s law of refraction n1sinɸ1=n2sinɸ2. N1=index of refraction in air which is equal to 1, ɸ1 is the angle of incidence and ɸ2 is the angle of refraction after light passed through the second medium, which is the glass.

Fig 1. sinɸ2 vs. sinɸ1 for plane surface

                The slope in the graph is the index of refraction since the equation follows a linear equation. The difference in the slope and the calculated index of refraction is due to the uncertainty error of ±0.5 in all the measured angles of refraction.

                The procedure for flat surface was repeated with the curved surface of the glass as coincident to the component axis of the optical disk. The results are the following:

Table W3. Reflection and refraction in glass with incident ray striking the curved surface.

Angle of incidence	Angle of reflection	Angle of refraction	Index of refraction
10°	10°	14°	0.717786115
20°	20°	30°	0.684040286
30°	30°	47°	0.68366373
40°	40°	70°	0.684040286
50°	50°	-
			Ave= 0.692382604

Fig 2. sinɸ2 vs. sinɸ1 for curved surface

The difference in the slope value and the calculated index of refraction was due to the uncertainty measurement of ±0.5 in all the angle of refraction values.

The next part of the experiment was observing total internal refraction using the curved surface used in the previous step. The optical disk was rotated until the refracted ray was parallel to the flat surface. At this point, the angle of incidence was the critical angle.

Table W4. Total Internal Reflection

Critical angle	45°
Index of refraction of glass n	0.707
Speed of light in the semicircular glass	424,328,147.1

The index of refraction was again calculated using Snell's Law with n1=the index of refraction for air=1, so the equation becomes sin 45/sin 90, the critical angle and angle of refraction, respectively. 

Total internal reflection was possible since the index of refraction n2<n1. 

The last part of the experiment was ray tracing for different refracting media.

The results were the following:

A.

B

C

D

E

References:

(1) Young, H. D., Freedman, R. A., Ford, A. L., & Sears, F. W. (2004). Sears and Zemansky's university physics: With modern physics. San Francisco: Pearson Addison Wesley.

The experiment was  interesting kaya lang mejo antok ako nun kasi kulang sa tulog :(
Ang fun gamitin nung materials :D