# PHYSICS 121 Experiment 8

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The Mechanical Equivalent of Heat
The purpose of this lab is to measure the conversion factor between mechanical energy and heat energy.

Equipment
1 1 1 1 1 1 1 1 1 spring balance thermometer stirring rod inner brass cup outer brass cup small clamp (check limitation of screw) large C-clamp pliers to tighten clamp crank with gears , turning black cylinder extra thermometer for the TA

small clamp pressing lid

Fig 1a. Apparatus disassembled.ag ainst cylinder inner brass cup removed from disk

rotating black cylinder, holds brass cups during run

crank friction occurs between these cups, sliding against each other outer brass cup dismounted from black cylinder stirring rod thermometer

spring balance

disk

large C-clamp holding setup tightly to table

Fig 1a. Apparatus disassembled.

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small clamp pressing disk with inner brass cup attached against outer brass cup attached to rotating cylinder, controls amount of friction spring balance thermometer along axis of rotation stirring rod disk attached to inner brass cup string attached to spring balance and disk outer brass cup attached to rotating cylinder rotating cylinder groove for string inner brass cup attached to disk

pulley

crank driving gears

Fig. 1 b Apparatus assembled.

Introduction
Historically, the relationship between heat flow into a material and its resulting temperature change was deduced prior to mankind‟s understanding of heat as a form of energy. A unit of heat (the calorie) was invented to quantify heat flow. A calorie is defined as the amount of heat necessary to raise the temperature of one gram of water by one degree Celsius. The equivalence of heat energy and mechanical energy can be deduced by measuring for example the amount of heat created when an object undergoes a known amount of work due to a frictional force. We will use this technique to measure the proportionality constant between the heat unit calorie and the energy unit Joule.

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Quantitative determination of the amount of work done and the amount of heat generated:

Figure 2 A simple schematic diagram of the apparatus is shown above in Figure 2. The inner brass cup is partly filled with water. The outer brass cup is connected to a crank handle and turned about the axis of rotation shown. The inner cup is stationary. Thus, with the inner cup lowered into the outer cup, there is friction. The work done by the frictional force is converted to heat. The meachanical work done (in Joule) and the heat generated (in calories) are measured and thus the conversion factor between the 2 units determined. If you apply a constant torque  to a disk with radius R by applying a constant force F tangentially to the disk, the torqe is given by  = F R (see the drawing in Ch 8 sheet 21 and the formula on sheet 23). The work done by turning the disk through an angle is given by W =  ( see Ch8 sheet 38). If N turns were made this angle is (N 2) radians. Enter the equation for the work into your REPORT SHEET, replace the torque by (F R), replace the total angle turned by (N 2) and label the resulting equation for the work as equation (1) of this lab. Explain all variables of the equation. In your experiment you don‟t turn the disk holding the inner brass cup, but you turn the outer cup with a crank and hold the disk stationary with a string exerting a force, which is measured by a spring balance attached to the string. The frictional force between the two cups does not set the inner cup and disk in motion, but is balanced by the force in the string. Thus the formula (1) in your REPORT SHEET worked out above is valid for the way you execute the experiment. The amount of heat input to the system can be analyzed by measuring the change in the temperature of the system. In general, the amount of heat absorbed or released by a single material, which does not undergo a phase change (Ch13 sheet 14), can be calculated by using the equation given in Ch 13, sheet 8. Enter this equation into your REPORT SHEET, label it as

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equation (2) of this lab and explain the variables of the equation. In your equation (2) and for this lab, use the Greek letter, δ, to denote „change‟, do not use Δ to denote change. Δ will be used to denote errors.

Procedure:
Disassemble the apparatus by moving the small clamp pressing against the disk off the top of the aluminum disk. The stopper in the middle of the aluminum disk contains a thermometer and a stirring rod; remove the stopper from the middle. Gently remove the thermometer and the stirring rod from the stopper. Unscrew the two screws on top of the aluminum disk. Pull out the inner and outer brass cups. Using a scale, obtain the following mass values: mb = mass of inner brass cup and outer brass cup ms = mass of stirring rod mth = mass of thermometer Assume that each mass measurement has an absolute error of 0.2 grams. Enter all values into your REPORT SHEET. Add cold water (roughly 6-8°C below room temperature) to the inner brass cup so that it is 90% full. After you have added the water, put the inner and outer brass cup on a scale and get the total mass of the cups plus water. To get the mass of the water, mw, subtract mb from this total mass. Assume this measurement has an absolute error of 0.2 grams and enter all values into your REPORT SHEET. Measure the diameter, D, of the aluminum disk with a ruler and assume that it has an absolute error of 2 mm. Q1: When measuring the diameter of the disk, do you want to measure the full diameter of the disk, why or why not? (Hint: where does the string sit on the disk ?) Reassemble the device with the inner cup filled with the water.Make sure that there is a piece of paper between the inner and outer cup during reassembly so that the crank will turn smoothly. Make sure that the string is sitting in the grooves of the aluminum disk and of the pulley. The pulley should be aligned as shown. YES NO

disk string pulley Figure 3. There should be a slight torque on the spring, i.e. the arrow pointing away from 0, when the string is hooked up to the spring balance. Clamp the aluminum disk down tight with the black

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Analysis:
Calculate the temperature change of the system and its error according to expression (6) in “Error and Uncertainty” (“EU”). Enter them into your REPORT SHEET.

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PHY 121

REPORT SHEET ( to be signed by instructor)

EXPERIMENT 10 : The Mechanical Equivalent of Heat
Name: ________________________________ Section:____________ SB#: ________________________ Date: ______________________ Lab Instructor:___________________________
Part I Quantitative determination of the amount of work done and the amount of heat generated: Equation (1) (including the explanation of the torque calculation): ________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

Equation (2): __________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ] Δmb: __________________[ ] ] ] ] Δms: __________________[ Δmth: _________________[ Δmw: _________________[ ΔD: __________________[

mb: _______________[ ms: _______________[ mth: ______________ [ mw: ______________ [ D:________________[

] ] ] ] ]

Q1: ______________________________________________________________________________

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______________________________________________________________________________ ______________________________________________________________________________

Q2: ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

Room Temperature: _________________________________[ Ti: ______________________[ Tf: ______________________[ ] ]

] ] ]

ΔTi: __________________[ ΔTf: __________________[

δT  ΔT (show both calculations explicitly and give units):______________________________ ______________________________________________________________________________ ______________________________________________________________________________

Q3: ______________________________________________________________________________ ______________________________________________________________________________

Initial counter value: _______________________________ Final counter value: ________________________________ N: ______________________________________________ F: ______________________ [ ] ΔF: __________________[ ]

Q4: ______________________________________________________________________________ ______________________________________________________________________________

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______________________________________________________________________________

Q5: ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ W  ΔW (show both calculations explicitly and give units): _____________________________ W = _________________________________________________________________________ ______________________________________________________________________[ ]

W =_________________________________________________________________________
______________________________________________________________________[ ]

Q6: __________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

Table 1: Specific Heat, Ci [cal g-1 °C-1] 1.000 0.092 0.215 0.200 ΔQi [

Material water brass aluminum (stir rod) glass (thermometer)

Qi [

]

]

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Explicitly show your calculations of Qw (for the water) and its error and give units: ___________
QW =_________________________________________________________________________

_____________________________________________________________________[

]

 QW =_______________________________________________________________________
_____________________________________________________________________[ ]

Explicitly show calculations of the total heat Q and its error and give units (neglect the error due to the stirring rod and the thermometer): Total heat Q =__________________________________________________________________ _____________________________________________________________________[ ]

Q =_________________________________________________________________________

__________________________________________________________________ __[ Klab  Δ Klab (show both calculations explicitly and give units): __________________________ Klab =________________________________________________________________[ Δ Klab = _____________________________________________________________________ _____________________________________________________________________[

]

]

]

Q7: _________________________________________________________________________ _____________________________________________________________________________

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