PHYS 112NAME:

SECTION:

Laboratory 1 Pre-Lab (value: 2 marks)Submit to your lab instructor ALONG WITH YOUR LAB at the END of the lab period.

1. Perform the following calculations using the rules for significant figures (see PHYS 111L):(a) 9.47 + 1.5 (b) 4.0 - 1.991 (c) 124/3 (d) 203 ⇥ 1.1356 (e) (2 + 2.4)/1.2

2. Determine, with proper units and significant figures, the masses shown in the images below.

3. The sum of all energy changes in a closed system must equal. . . ? Why? What principle is this?

4. Rewrite Equation 2 to solve for cb. Show your steps.

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PHYS 112VANCOUVER ISLAND UNIVERSITY

Department of Physics, Engineering and Astronomy HT 1

Laboratory 1:Specific Heat & Latent Heat

Experiments are to be completed on the provided laboratory sheets below; any supporting material(eg. graphs) should be attached. Make sure your name and your partners name(s) are clearlyindicated on the front page of your lab. Neatness and clarity count! Explain your answersclearly and concisely. If an equation is to be used in a calculation, write the equation down andthen insert numbers and solve. Report your final answer to the appropriate significant figures.

The lab write-up is due by the end of the lab. Late labs will not be accepted.

APPARATUS

Double styrofoam cup calorimeter with lid, stir stick (plastic knife), 500 mL plastic jug, short digitalthermometer, hot-plate with large beaker and thermometer, wire hooks, triple-beam balance, cubedice, hand warmers, drinking bird with small beaker, metal samples (copper, zinc, or tin).

OBJECTIVE

1. To determine the specific heat of a metal.

2. To observe the e↵ect of the latent heat of cystallization.

3. To determine the latent heat of fusion of water.

THEORY

Specific Heat

Heat is a transfer of energy. If energy is added to a body, the kinetic energy of its atoms ormolecules is increased and the temperature of the body increases. The relationship between Q, theheat added to a substance, and �T = Tf � Ti, the temperature change, is given by

Q = mc�T (1)

where m is the mass of the body, and c is a constant called the specific heat which is characteristicof the material. The SI unit of specific heat is J/kg�C.

If two bodies, a and b, which are initially at two di↵erent temperatures, Tai and Tbi, are in thermalcontact and are isolated from the outside environment, the warmer body will cool o↵ and thecooler body will warm up until the two arrive at a common final temperature, Tf . According tothe principle of conservation of energy, the amount of thermal energy lost by the warmer body

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PHYS 112 HT 1

must equal the amount of thermal energy gained by the cooler one. Another way of expressing thisis to say that the sum of the energy changes in a closed system must be zero, that is,

XQ = 0

In the case of the two bodies, a and b,

Qa +Qb = 0

and therefore, substituting from Equation 1,

maca(Tf � Tai) +mbcb(Tf � Tbi) = 0 (2)

Minimizing heat exchange with the environment

A body whose temperature is di↵erent from that of the environment will either gain heat from theenvironment or lose heat to it. Even if an insulated container is used in an experiment, there willstill be some heat energy exchanged. One way to minimize the exchange of energy is to perform theexperiment over a temperature range which is symmetric about the environmental temperature,for example, starting ten degrees above room temperature and ending ten degrees below roomtemperature. If this is done, then the system will lose a small amount of heat to the environmentwhile it is above room temperature and gain a small amount when it is below room temperature.If the times spent above and below room temperature are equal, then the gains and losses shouldbe the same and should cancel out. This technique is used in the present lab experiment.

If heat is exchanged with the environment then Equation 2 becomes

maca(Tf � Tai) +mbcb(Tf � Tbi) +Qenv = 0 (3)

where Qenv is positive if heat is lost to the environment (i.e. environment heats up) and negativeif heat is gained from the environment (i.e. environment cools down).

Latent heat of fusion

If a substance in the solid state is to melt, heat energy must be added to it in order for the moleculesto break free of the bonds which hold them together in the rigid framework of the solid. Conversely,if a liquid is to freeze, the molecules of a liquid must have enough of their kinetic energy removed sothat they can take their places in the structure of the solid. The energy di↵erence, per unit mass,between the liquid and solid states is called the latent heat of fusion. This phase change takesplace at a well-defined temperature called the melting point (or freezing point).

The amount of heat required to melt a given mass of any solid is

QF = mLF (4)

where m is the mass of the solid (and the resulting liquid), and LF is its latent heat of fusion.The SI unit of latent heat of fusion is J/kg. The energy change QF is positive if a material meltsbecause energy is added to the material and negative if it freezes because energy is removed.

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DATE:NAME:

PARTNER:

Laboratory 1:Specific Heat & Latent Heat

Part A: Specific heat from thermal equilibrium measurements

1. Place three pieces of one kind of metal in the water bath on the hot-plate and let them heat for

at least ten minutes. Record the type of metal used: .

2. [0.5 marks] Insert the thermometer into the blue foam lid and leave it there for the remainderof the experiment. Record the mass (in grams) of the empty calorimeter without the lid.

mass of empty calorimeter: mcal = .

3. [1 mark ] When you are ready to add the metal, fill the calorimeter with cold (⇠14�C)tap water su�cient to completely submerge the metal & record the mass without the lid. Recordthe water temperature; the digital thermometer measures temperatures to the nearest 0.1�C.

mass of calorimeter & water: mcal+water = .

initial temperature of water: Twi = .

4. [0.5 marks] Record the temperature of the hot water bath/initial temperature of the metal.

initial temperature of metal: Tmi = .

5. [0.5 marks] With as little delay as possible remove the metal pieces (one at a time) fromthe hot bath, BRIEFLY PAT them dry with a paper towel, and place them in the calorimeter.Place the lid on the calorimeter. Ensure the thermometer is in the water and not touch-ing the metal or poking a hole in the calorimeter. Stir the water slowly and continuously.Record the maximum steady (final) temperature reached by the system.

final temperature of system: Tf = .

6. [0.5 marks] Remove the lid and record the mass of the calorimeter and its contents.

mass of calorimeter, water & metal: mcal+water+metal = .

7. [2 marks] From your measurements above, calculate the mass of the metal and the mass of thewater in the calorimeter. Clearly show your steps/work (use meaningful labels) and watch sig figs.

mass of metal: mm =

mass of water: mw =

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PHYS 112 HT 1

8. [1 mark ] Starting fromP

Q = 0, derive the conservation of energy equation for the system INSYMBOLS, i.e. Equation 2. Use descriptive subscripts given (e.g. w = water, m = metal, etc.).

Rewrite your equation to yield an expression for the specific heat of the metal, e.g. cm = . . ..

9. [1.5 marks] Using your equation above, calculate the specific heat of the metal. Assume thespecific heat of water is cw = 4180 J/kg�C. Show ALL equations/work/steps; watch your sig figs.

specific heat of metal: cm = .

10. [1 mark ] Compare (percent deviation) your value of the specific heat cm for the metal you usedto its accepted value (copper: ccu = 385 J/kg�C, zinc: czn = 388 J/kg�C, tin: csn = 228 J/kg�C).

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PHYS 112 HT 1

11. [1 mark ] Write the conservation of energy equation for the system including the environ-ment IN SYMBOLS, i.e. Equation 3. Use descriptive subscripts as previously.

Rewrite your equation to yield an expression for the specific heat of the metal, e.g. cm = . . .. Theright-hand side of your expression should be in a form including a Qenv term in the numerator.

12. [1.5 marks] What is the sign of the percent deviation in part 10? Is your calculated valueof cm too low or too high? Using this information and your equation above, is Qenv positive ornegative (i.e. has heat been gained from or lost to the environment)? Explain your reasoning.

Part B: Latent heat of fusion

1. [1 mark ] Record the mass of the empty calorimeter and the ambient (room) temperature (usingthe digital thermometer).

mass of empty calorimeter: mcal = room temperature: Troom = .

2. [0.5 marks] Half-fill the calorimeter with warm water (⇠10�C above Troom) & record the mass.

mass of calorimeter & water: mcal+water = .

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PHYS 112 HT 1

3. [0.5 marks] Insert the thermometer and stirrer into the blue foam lid and place it on thecalorimeter. Stir the water and record its temperature.

initial temperature of water: Twi = .

4. Dry an ice cube with some paper towel and add it to the calorimeter; avoid touching the icewith your fingers once it has been dried. Stir the mixture slowly and continuously as the ice melts.

5. [0.5 marks] Continue adding and melting ice one cube at a time UNTIL the temperature is asfar BELOW room temperature as the initial temperature was ABOVE room temperature. Removeany remaining chunks of ice left in the calorimeter at that point and record the temperature.

final temperature: Tf = .

6. [0.5 mark ] Remove the lid and record the mass of the calorimeter and its contents.

mass of calorimeter, water & ice: mcal+water+ice = .

7. [2 marks] From your measurements, calculate the masses below. Show your steps/work/labels.

mass of water: mw =

mass of ice: mi =

8. Tidy the apparatus and turn the thermometer o↵.

9. [1.5 marks] Starting fromP

Q = 0, derive the conservation of energy equation IN SYMBOLSONLY for the ice & water system. Use descriptive subscripts (e.g. w = water, i = ice, etc.). Yourequire 3 terms: the temperature change of the warm water, for the (melted ice) water, and for thephase change from ice to water.

Rewrite your equation to yield an expression for the latent heat of fusion LF , e.g. LF = . . ..

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PHYS 112 HT 1

10. [1.5 marks] Calculate the value of the latent heat of fusion of water using your equationabove. Assume that the specific heat of water is cw = 4180 J/kg�C and that ice melts at 0�C.

latent heat of fusion of water: LF = .

11. [1 mark ] Compare (percent deviation) your value to the accepted value Lf = 3.33⇥ 105 J/kg.

12. [1 mark ] Calculate the average of your initial & final water temperatures. What do you expectQenv to be if your average water temperature is close to room temperature? Why?

13. [1 mark ] In the calculation of the latent heat of fusion, the ice was assumed to be at 0�C whenit was added to the calorimeter. Is this a reasonable? How can you tell by looking at the ice?

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PHYS 112 HT 1

Part C: Latent heat of crystallization

This part of the lab is a demonstration of the latent heat of crystallization of a super-cooled sodiumacetate solution found in some brands of hand-warmers. While this is not a true phase change asdiscussed in the Theory, it is analogous and serves to illustrate the concept. The reaction is re-versible in that the substance may be heated to re-dissolve the crystals.

1. [1 mark ] Describe the initial appearance & approximate temperature of the hand warmer.

2. [1 mark ] Press the indicated spot firmly with your finger. Describe the result IN DETAIL.

3. [1 mark ] Where does the heat come from (do NOT simply say “exothermic reaction”)?Hint: consider what is happening to the motion of the molecules as they change from liquid to solid.

Part D: Drinking bird

Inside the evacuated glass bulb are both the liquid AND gas phases of the substance dichloromethane,which has a low boiling point (39.6�C). If the vapour phase inside the tube is cooled some condenses.

1. [1 mark ] Consider the (stationary) bird in its stand. Is the centre of gravity of the bird aboveor below the pivot point? Explain your reasoning fully & clearly.

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PHYS 112 HT 1

2. [2 marks] Initially, is the vapour pressure in the tube greater than, less than, or the same asthe vapour pressure in the lower bulb? How can you tell by looking at the fluid/gas interface?

Soak the bird’s head in a small beaker of room temperature water. What happens to the tempera-ture of the vapour in the upper bulb as the water evaporates from the bird’s head? Explain briefly.

What does the liquid in the tube start to do shortly after the bird’s head was soaked? Why?

At what point does the bird tip over? Where is the centre of gravity at this moment? Explain.

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PHYS 112 HT 1

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