Lab work

PREDICTIONS

Question 10 The units of work are Joules, which are abbreviated as J, or alternatively Nm. Question 11 See graph attached at the end.

Heating Water by doing Work

Thomas Gredig∗

Department of Physics and Astronomy, California State University Long Beach, CA 90840 (Dated: July 7, 2016)

An article usually includes an abstract, a concise summary of the work covered at length in the main body of the article. It is used for secondary publications and for information retrieval purposes.

I. INTRODUCTION

Energy is a conserved quantity and therefore very use- ful. Energy has many forms amongst them, we have ki- netic energy, rest energy, potential energy, electric po- tential energy, and heat. The total amount of energy is conserved or stays constant. The total energy is the energy from the system plus the energy from the sur- rounding. The system’s energy can be changed by work, which can be mechanical work. In this experiment, we will convert mechanical work into heat by shaking a box with water.

∆E = mC∆T (1)

where m is the mass of a material, C is the specific heat of the material and ∆T is the change in temperature.

II. EXPERIMENT

Tap water is poured into a plastic container and weighed with a kitchen scale set to metric units. Care- fully removing the weight of the plastic container, the amount of water is determined to be m = 19 g, see Fig. 1. The water temperature is measured using a digital ther- mometer. The water is then shaken for a certain amount of time, see Table I, over a range of 0.3 m. This was re- peated 4 times to check that the results are reproducible. Small deviations of about 0.1 ◦C were observed. The ex- periment could have also used the Arduino temperature sensor to measure the water temperature.1

III. RESULTS

A total of 4 shake trials were made, see Table I. For each trial, the temperature was measured 5 times in or- der to average fluctuations in the temperature. The num- ber of shakes ranged from 0 to 150 and the temperature changed by a total of 1.4 ◦C.

FIG. 1. Water is poured into a plastic container and weighed on the scale. The temperature of the water is measured with digital temperature sensor

TABLE I. Set of measurements shaking the water container a number of times listed as ”Shakes”. The temperature was measured 5 times for each trial and averaged as it fluctuated by 0.1 ◦C

Trial Shakes Temperature (◦C)

1 0 24.4 2 100 24.4 3 1000 25.6 4 1500 25.8

IV. ANALYSIS

From Equation 1, we find that the energy change ∆E is given by the mass, specific heat, and the temperature change. For water, we are using C = 4180 J/(kg K). Con- servation of energy tells us that ∆Esys = Wsurr. Using our values, we determine the change in energy.

∆E = mC∆T = 19 g · 4180 J/(kg K) · 1.4 K = 111 J (2)

The mechanical work can be computed by making some assumptions about the shaking. We estimate that

2

FIG. 2. This shows that more shakes increase the temperature of the water. The blue line is a linear fit to the data.

the average pathway is about 0.3 m, since the hand moves to the right and then the left. That would give the fol- lowing result:2

W = F ∆x (3)

The distance ∆x is increased by the number of shakes. With each shake the hand moves by about 0.6 m, so that the total distance for trial 4 is 900 m. The force is esti- mated from the acceleration which can be approximated as an oscillation. In this case, we measured that vigor- ous shaking involves 4 arm motions per second, giving an approximate acceleration 10 m/s2.

TABLE II. Work computation from the four trials using the relation that W = F ∆x and assuming that an average force.

Trial Shakes Work (J)

1 0 0 2 100 11 3 1000 114 4 1500 171

Table II shows that the work that goes into the shak- ing process of the water is larger than the energy required to heat the water. The reason is that some mechanical energy was converted into other energy components, in- cluding sound. It is also possible that the warm hands transferred some of the energy.

V. SUMMARY

Mechanical work can be transferred to other energy forms, such as heat. In this experiment, water is shaken mechanically and the change in temperature measured. The water is vigorously shaken for a large number of times and the work is computed and compared with the energy needed to heat the water. It was found that water can be heated with mechanical work. Despite the poor knowledge of the acceleration, the order of magnitudes agreed. Some of the mechanical energy was converted to sound as well.

VI. ACKNOWLEDGEMENT

The work was done on June 24 and without the help of anyone else.

BIBLIOGRAPHY

∗ thomas.gredigcsulb.edu 1 W. J. Esposito, F. A. Mujica, D. G. Garcia, and G. T. A.

Kovacs, in 2015 IEEE Signal Processing and Signal Process- ing Education Workshop (SP/SPE) (2015) pp. 301–306.

2 R. W. Chabay and B. A. Sherwood, Matter and Interac- tions, 4th ed. (Wiley, Hoboken, NJ, 2015).