Experiment 2L Joule's Law - St. John's University



Experiment 21: Joule’s Law

Purpose

1) To observe the release and absorption of Joule Heat.

2) To measure Joule’s Constant J.

Apparatus

(a) an electric calorimeter, a DC power supply (high power)

(b) an ammeter, a timer, a glass beaker, an equal arm balance with weights

Theory

|A) Joule Heat. An electric current I passing through an ohmic resistor R |(1) |BASIC FORMULA |

|releases electric power P given by formula (1). If I is in amperes and R | | |

|is in ohms then P is in watts. In a time interval Δt (in seconds) an | | |

|amount of energy ΔE=P · Δt (in joules) will be released, in the form of Joule | | |

|Heat. | | |

| | |P = I2 · R |

|B) JOULE’S CONSTANT. The released heat is absorbed by the core |(2) |BASIC RELATION |

|of the calorimeter. | | |

|The amount of absorbed heat ΔQ (within a | | |

|time Δt) is given by relation (2) where: | | |

| | |ΔQ = (MW·CW+MCal·Ccal) ·ΔT |

MW = mass of the water

CW = specific heat of water.

Mcal= mass of the inner cup and stirrer of the calorimeter

Ccal = specific heat of the inner cup and stirrer

ΔT = change in temperature during the time interval Δt

| Traditionally, ΔQ is expressed in calories. |(3) |PRACTICAL FORMULA |

|This applies if MW and Mcal are in grams, | | |

|ΔT is in degrees Celsius (‘deg’)(, and | | |

|CW and Ccal are in cal/gm deg. | | |

| | |J = I2R |

| | |(MW·CW+MCal·Ccal) [pic] |

To relate ΔQ in calories to the supplied energy in joules, a conversion factor J is needed. We write ΔE = J · ΔQ, as well as ΔE = P · Δt and this leads to formula (3).

Preliminary Procedure

a) Your Lab Instructor will explain to the class the operation of

(i) The High-Power DC supply. Observe that you can control your current only in steps!

(ii) The electric calorimeter. Pay attention to the correct way of stirring!

(iii) The Timer; make sure you understand the importance of a rapid start of each run.

b) If your work with a partner, here are the suggested tasks in a run:

First student: A quick (in 2-3 seconds) selection of the proper current; monitoring the timer and the ammeter.

Second student: Proper stirring of the calorimeter, and an accurate reading of the thermometer.

After a completed run, partners should switch their duties.

|c) These tasks should be done by both |[pic] |

|partners together, verifying each other’s | |

|performance: Measure and record the mass Mi of the | |

|inner cup. Set the voltage of the power | |

|supply to zero and the power OFF. | |

|Assemble the circuit as in Fig 1. Set the ammeter | |

|scale at 5 amps and | |

make sure that the positive and negative

terminals are connected as shown.

|d) On your data sheet, prepare a table |Run #1 |Run #2 |Run #3 |

|as shown. You will need up to about | | | |

|25 lines. Make sure you can read the thermometer | | | |

|at a glance, to an | | | |

|accuracy of 0.5 deg. | | | |

| | | | |

|DO NOT PROCEED BEYOND THIS POINT WITHOUT INSTUCTOR’S | | | |

|APPROVAL. | | | |

| |I = amp |I = amp |I = amp |

| |t |T |t |T |t |T |

| |(min) |(deg) |(min) |(deg) |(min) |(deg) |

| |1 | |1 | |1 | |

| |2 | |2 | |2 | |

| |3 | |3 | |3 | |

| |4 | |4 | |4 | |

| |……. | |……. | |……. | |

Procedure

e) Use the beaker to obtain roughly 250 cm3 (250 ml) of cold tap water. Pour it

into the inner cup. Measure and record the total mass Mi + MW. Close the

calorimeter, making sure that the stirrer can operate correctly.

Observe that the thermometer reading will decrease until it stabilizes (after a

few minutes) at the tap water temperature, whatever it might be. In the meantime, plug in your power supply and timer, both still OFF.

f) Turn the power ON. There should still be no current (because the voltage must still

be zero). Make all final checks before beginning your Run #1.

Start the timer, and at the same time (within 2-3 seconds) adjust the current to

be as close as possible to 5 amps, but not beyond the scale. At the same time begin

stirring the calorimeter, and keep stirring it, slowly but steadily, throughout the run.

g) At each one minute interval, record the thermometer reading. Read it quickly (2-3 sec), with to 0.5 deg accuracy. Continue the run until about 50°C is reached. (It

should take about 15 min.)

During this time keep watch on the ammeter. The current should stay constant

(within 0.01 amp.) during the run(. Record its value, with three significant digit accuracy.

After completing the run, turn OFF the power and set the voltage to its

MINIMUM (zero). Discard the water from the calorimeter and wipe its interior

with a paper towel.

h) For run #2 repeat item (e), recording the new value of Mi + MW. Then proceed as in

(f) except setting the voltage knob one step lower than in run #1. Proceed as in (g),

recording the new value of the current. You may stop the run at about 45°C.

j) For run #3 repeat (h) but set the voltage knob another step less. Record the current. You may stop at 40°C.

k) Apart from Mi, the calorimeter mass Mcal should include the mass of the stirrer,

to be taken as 9 grams. Both of them are made of aluminum, so that we can say that Ccal = 0.215 cal/gm deg. mThe resistance of the calorimeter coil is to be taken as

R = 1.245 ohms.

Record these values on your data sheet.

BEFORE YOU LEAVE THE LAB:

(i) Make sure that you have recorded ALL the data you will need in your report.

(ii) Dispose of water from your calorimeter, wipe dry its interior, and leave it

open.

(iii) Unplug your electrical appliances, return the connectors to their proper boxes, and clean up your station.

Lab Report

1) For each run, draw a graph of T vs. t on a separate sheet of graph paper, using the

entire sheet (see page v of this Handbook). Suppress the origin of the vertical axis

(T axis). Display the measurements of ∆T and ∆t and the calculation of slope, quoting

their physical units.

2) Show your value of Mcal · Ccal , quoting physical units.

3) Summarize your results in a table (don’t forget to put units for all quantities!):

|Run |I |P |Slope [pic] |MW |MW CW + Mcal · Ccal |J |

|# | | | | | | |

|1 | | | | | | |

|2 | | | | | | |

|3 | | | | | | |

| | | | | | Average: | |

4) Compare your average measurement of Joule’s Constant with the correct value of

4.18 joule/cal, by finding the % discrepancy.

5) Answer the following questions:

Q #1: In Run #1, how long would you expect to wait, starting from the

moment of turning ON the power, until the water begins to boil?

Show your calculation.

Q #2: In Run #1, how long would you expect to wait, starting from the

moment of turning ON the power, until all water boils off? Show

your calculation.

( A degree on the Celsius (Centigrade) temperature scale is the same as a Kelvin (K). We use ‘deg’ to avoid confusion with the Absolute Temperature scale.

( If not, the most likely reason is loose connections. Check them, tighten all socket screws, and check the fitting of connectors into sockets. Repeat the run. Call your lab instructor if necessary.

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