08 Specific Heat Capacity

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Specific Heat Capacity

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PRERE-L-LABAB A ASSIGNMENTSSSIGNMENTS::

To be assigned by your lab

To be assigned by your lab instructor.instructor.

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STUDENTTUDENT L LEARNINGEARNING O OUTCOMESUTCOMES::

•• The First Law of ThermodynamicsThe First Law of Thermodynamics

•• Thermal energy as a function of temperatureThermal energy as a function of temperature

•• The units of energyThe units of energy

•• Sign conventions in heat flowSign conventions in heat flow

•• Heat capacityHeat capacity

•• Specific heat capacitySpecific heat capacity

•• Factors in experimental error Factors in experimental error

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EXPERIMENTALXPERIMENTAL G GOALSOALS::

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Yoou u wilwill l meameasursure e the specithe specific heat capacfic heat capacity of ity of a a knoknown metalwn metal. . TheThen n yoyou u wilwill l meameasursure e thethe specific heat capacity of an unknown to identify the metal.

specific heat capacity of an unknown to identify the metal.

IINTRODUCTIONNTRODUCTION::

Heat Capacity Heat Capacity



 larlarge ge parpart t of of chechemismistry try is is stustudyidying ng and and undeunderstrstandianding ng the the phyphysicsical al and and chechemicmicalal changes that mat

changes that matter undergoter undergoes. es. The driviThe driving force for most chemical and physicang force for most chemical and physical changes isl changes is energ

energyy! often in the ! often in the form of thermal enerform of thermal energy "heat#gy "heat#. . TeTempermperature and heat are not ature and heat are not the samethe same $ua

$uantintityty. . The temThe temperperatuature of re of an ob%ect is an an ob%ect is an indindicaicator of the tor of the amoamount of unt of thethermarmal l eneenergy itrgy it &possesses'! but

&possesses'! but heat is heat is a measure of a measure of the transfer the transfer of energy of energy to or to or from an from an ob%ect. ob%ect. (e (e know thatknow that the more a

the more a substsubstance is heated! the more its temperatance is heated! the more its temperature will rise. ure will rise. This relaThis relationstionship is a hip is a direcdirectt proportionality that may be expressed as

proportionality that may be expressed as qq∝∝∆∆T T _{! where $ is the heat absorbed or released by the}_{! where $ is the heat absorbed or released by the}

system

system and )T is its temperature change ")T *T and )T is its temperature change ")T *Tfinalfinal + T + Tinitialinitial#. #. This proportThis proportionality may ionality may be also be also bebe written as an

written as an e$uality!e$uality!

constant constant = = ∆ ∆T T q q or or qq ==constantconstant⋅⋅∆∆T T _,-_,-

The constant of proportionality is the

The constant of proportionality is the heat capacityheat capacity!! C C _{! and is defined as the $uantity of heat}_{! and is defined as the $uantity of heat}

re$ui

re$uired to red to change an ob%ect/change an ob%ect/s temperats temperature by ure by one unit of one unit of temptemperaturerature e "usu"usually -ally - oo_{0 or - 1#.}_{0 or - 1#.} Hence we can rewrite 2$uation - as

Hence we can rewrite 2$uation - as

T T C C q q == ⋅⋅∆∆ _,3_,3 45 45

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6t follows that heat capacity has units related to _temperaturenergy _e and is commonly expressed as

C J

o "also written as 7890 or 7 90 :-_#.

The heat capacity of a system is dependent on a few factors. The heat capacity is dependent on the amount of a sample present as shown in Figure -! and is thus an extensive property; a larger amount of sample re$uires more heat than a smaller amount of the same

substance to raise the substance/s temperature by one unit. 6n addition to the amount of substance present! the kind of substance has a direct bearing on its heat capacity. The same amounts of different substances usually have different heat capacities! and heat capacity is often used for samples of a fixed si<e. 6t would be more convenient if the heat capacity depended only on the type of material! and not the amount of material. 6f heat capacity were an intensive property! independent of the amount of substance! it could be used as an analytical tool to

identify a substance! much like density.

Fi!"e #$ Heat re$uired for -o_{0 change in temperature showing dependence} of heat capacity! C ! on amount of substance.

Specific Heat Capacity

6n order to overcome the fact that heap capacity varies with the amount of a substance! chemists often use the %pecific heat capacity! C _%_{! also known as the specific heat. The specific}

heat capacity of a substance is defined as the amount of heat re$uired to raise the temperature of - gram of the substance by -o_{0 "see Figure 3#.}

=.->= 7 - g H₃? 33.@°0 35.@°0 4= 100 g 200 g C * $ C' * 3$

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Fi!"e &$ Specific heat capacity.

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The relationship between the thermal energy and specific heat capacity may be expressed as

T C m

q= ⋅ _s ⋅∆ _,5

2$uation 5 is similar to 2$uation 3 with the additional parameter of mass! m. The heat capacity! C ! of a given sample may be converted to its specific heat capacity! C s! by dividing the mass of the sample into C to give

g 3@@ B g -@@ C C C s = =

Cy accounting for the amount of substance! the specific heat capacity depends only on the kind of substance and is therefore an intensive property. This $uantity has units related to

e temperatur mass

energy

⋅ . The units of specific heat are commonly expressed as g C J

o

⋅

"also written

as 78gD90 or 7 g:-₉₀:-_#.

6n this laboratory! a calorimeter is used to measure the specific heat of various known metals.  calorimeter is an apparatus used to measure the heat released or absorbed by a physical or chemical process. The calorimeter used here is composed of a pair of stacked Styrofoam coffee:cups with a lid "see Figure 5 in the Erocedure section#. The lid has two holes! one for a thermometer and the other for a stirring wire! and helps minimi<e heat loss to the atmosphere. 6n addition to measuring the specific heat of a known metal! an unknown metal will be identified based on the determination of its specific heat capacity.

The specific heat can be determined by immersing a known mass of warm metal of a known temperature into a known volume of water! at a known! lower temperature. Heat energy will flow from the hot metal to the water until! after a period of time! the water and metal achieve the same temperature. From the First Law of Thermodynamics! the sum of the heat lost by the metal and the heat gained by the water in a perfect experiment is $metal  $water * @! which we can rearrange as

$metal * :$water ,=

The negative sign in 2$uation = comes about because of the )T term "see 2$uation 5#. The final temperature of the metal is lower than the initial temperature! and the resulting value of $metal will be negative. Cy convention! the flow of heat out of a body is a negative $uantity.

n ideal calorimeter would provide perfect insulation so that its contents! the system! could undergo its temperature change without any loss or gain of heat to the surroundings or to the calorimeter itself. Such a calorimeter does not exist. 6nstead! we must build an apparatus that gains "or loses# a minimum amount of heat energy itself while also minimi<ing the flow of heat into or out of the Gniverse. 2xperimentally! the total heat gained by the water that we measure will not be the actual heat lost by the metal since the apparatus will gain some of the heat as well as permit some leakage to the atmosphere. 6n this experiment! the heat lost by leakage to the atmosphere will be ignored! since the Styrofoam calorimeter is a reasonably good 4

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insulator. However! the heat lost by the system to the calorimeter is small! but not negligible! and it must be considered. (ith this correction! 2$uation = becomes

$metal * :"$water  $cal# ,A To determine calorimeter ! the heat capacity of the calorimeter! C cal ! must first be determined. (ith C cal ! the heat absorbed by the calorimeter may be accounted for in the determination of the specific heat of a metal. The determination of C cal is called the calibration of the calorimeter.

To calibrate the calorimeter! warm water of a known mass and temperature is mixed with a known mass and temperature of cooler water in the apparatus. 6n an ideal apparatus! the heat gained by the cooler water would exactly e$ual the heat lost by the warmer water. However! in the real world! the heat lost by the warm water will be e$ual to the heat gained by the cooler water plus heat lost to the calorimeter!

$lost by hot * :"$gained by cold  $cal# , Iearrangement yields

$cal * :"$lost by hot  $gained by cold# ,J which can be used to determine the heat capacity of the calorimeter.

6n this experiment! the actual calibration of the calorimeter will not be performed. 6nstead the C cal is given as >.5 78o0. (ith this value of C c al for the coffee:cup calorimeter! 2$uations 5 and A may be used to determine the specific heat of a metal. Table - lists the specific heat capacities of various metals.

Ta'(e #$ Specific heat capacities of various metals.

Meta( Specific Heat Capacity)C s *+,._C/ _Meta( Specific Heat Capacity)C s *+,._C/ Lead @.-34 0obalt @.=3-Kold @.-34 ickel @.=== Tungsten @.-53 6ron @.==4

Elatinum @.-55 0hromium @.=A@

eodymium @.-4- Manganese @.=J4

Tin @.33> Titanium @.A33

Silver @.35A Eotassium @.JAJ

Strontium @.5@ luminum @.>4J

0opper @.5>A Magnesium -.@3

Ninc @.5>> Sodium -.35

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SAMPLE CALCULATION OF THE CALIBRATION OF A CALORIMETER :

(ater with a mass of A@.@ g at >@.- o_{0 was added to A@.@ g of water at 3J.3}o_{0. Gpon mixing!} the final temperature attained was A-.4 o_{0. (hat is the heat capacity of the calorimeter! C}

cal O "ote; This example calculates the heat capacity of the calorimeter! whereas in the laboratory you will need to calculate the specific heat of the metal. The calculations are similar! but the distinction needs to be recogni<ed.#

Heat lost by warm water;

$lost * "A@.@ g#D"=.-> 78gDo0#D"A-.4o0 + >@.-o0# * :A>4@ 7 Heat gained by cool water;

$gained * "A@.@ g#D"=.-> 78gDo0#D"A-.4o0 + 3J.3o0# * A-@ 7 Heat absorbed by calorimeter;

$cal * :":A>4@ 7  A-@ 7# * J5@ 7 Heat capacity of calorimeter;

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= = 0 3 . 3J 0 4 . A-7 J5@   cal C _{34 78}o 0 PROCEDURE:

A$ Mea%!"e the C s .f a 01.21 Sa3p(e$

-. ?btain two nested coffee:cups. Nero the balance and weigh the empty! dry cups to the nearest milligram. dd approximately A@ mL of water to the cups and determine the mass of water by difference. ssemble the coffee:cup calorimeter as shown in Figure 5. First! insert the thermometer into the split stopper! and slide the stopper toward the top of the thermometer. ext! slide the thermometer into the center hole of the calorimeter lid. Elace the ring stand clamp on the stopper! and ad%ust the clamp on the ring stand to where it will hold the thermometer bulb about - cm from the bottom of the cup. Finally! insert the stirrer in the second hole of the lid with the loop encircling the bulb of the thermometer. (ait approximately A minutes before recording the temperature of the water to the nearest @.-o_0. 3. Measure the mass of a weighing boat! add approximately 5@ g of a known sample of metal!

and obtain the mass of the metal by difference. "The metals used should be large pieces of metalP metal shot and foil don/t work very well.# Transfer the sample into an appropriately si<ed test tube! ensuring that no sample is lost.

5. 6t is recommended that a trial run be performed in con%unction with your partner before data is actually recorded for steps = and A. You actions need to be swift and accurate to ensure $uality data "and resultsQ#! but safety cannot be compromised. Take the time to familiari<e yourself the procedure and determine the best way to execute it.

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=. To a 3A@:mL beaker! add approximately -A@ mL of water and bring to a rolling "but not violentQ# boil. ?nce the water is boiling! immerse the test tube containing the metal into the water using a clamp to support the test tube. fter R-@ minutes in the boiling water! the sample inside the test tube and the boiling water should be at the same temperature. Iecord the temperature of the water to the nearest @.- o_{0. Transfer} the thermometer to the calorimeter! and allow it to come to the same temperature that was recorded earlier.

A. Quickly transfer the hot metal in the test tube to the calorimeter containing the water. Take care to not splash any water out of the calorimeter! 6mmediately replace the lid! thermometer and stir wire! and record the temperature at time <ero. Kently stir the water with the wire and record the temperature in -A second intervals until the temperature decreases for at least five measurements. This may take a few minutes. 6t is extremely important that the water be constantly stirred throughout the experiment. Finally! record when the temperature is at a maximum! which will be immediately before the temperature begins to descend.

. Iepeats steps -:A! to determine if you obtain the same value for the specific heat of the known metal. Ieturn your metal sample to the waste container provided.

J. Gsing your data! compute the specific heat capacity! C s! of the known sample. lso report the percent error from the value listed in Table -. The specific of water! C s!water ! is =.-> 78g0! and the heat capacity of the calorimeter! C cal ! is >.5 78o0.

:qmetal * qwater  qcal

:"C s!metal  mmetal ∆Tmetal# * "C s!water  mwater ∆Twater #  "C cal  ∆Tcal#

∆T * Tf : Ti -@@ value true value# true : e "your valu error U = ×

B$ Mea%!"e the C s .f a1 U141.21 Sa3p(e$

>. Gse the same procedure for determining the specific heat of a known sample to determine the specific heat of an unknown sample. Ce sure to indicate which unknown you have.

44 3 nested Styrofoam cups clamp thermometer lid stirrer split stopper

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LAB R EPORT

Specific Heat Capacity

ame VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV Wate VVVVVVVVV Ieport Krade VVVVVV Eartner VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV Section VVVVVVVVV

A$ Specific Heat .f a 01.21 Meta($

-. Mass of the coffee:cups VVVVVVVVVVVV Mass of the cups  water VVVVVVVVVVVV Mass of the water VVVVVVVVVVVV Temperature of cool water VVVVVVVVVVVV 3. 6dentity of metal sample VVVVVVVVVVVV Mass of metal sample VVVVVVVVVVVV Temperature of boiling water VVVVVVVVVVVV 5. Time vs. temperature data + first run;

Time "sec# Temperature "90# Time "sec# Temperature "90# Time "sec# Temperature "90# @ -@A 3-@ -A -3@ 33A 5@ -5A 3=@ =A -A@ 3AA @ -A 3J@ JA ->@ 3>A 4@ -4A 5@@

Maximum System Temperature "Tf # VVVVVVVVVVVV

=. 0alculate the specific heat of the known and percent error . Show workQ C s = VVVVVVVVVV 78gDo0 U error * VVVVVVVVVVVV -@@

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A. Mass of the coffee:cups VVVVVVVVVVVV Mass of the cups  water VVVVVVVVVVVV Mass of the water VVVVVVVVVVVV Temperature of cool water VVVVVVVVVVVV . 6dentity of metal sample VVVVVVVVVVVV Mass of metal sample VVVVVVVVVVVV Temperature of boiling water VVVVVVVVVVVV J. Time vs. temperature data + second run;

>. 0alculate the specific heat of the known and percent error . Show workQ C s = VVVVVVVVVV 78gDo0 U error * VVVVVVVVVVVV

4. verage specific heat of the known and percent error .

C s = VVVVVVVVVV 78gDo0 U error * VVVVVVVVVVVV

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-@-B$ Specific Heat .f a1 U141.21 Meta($

-. Gnknown umber VVVVVVVVVVVV Mass of the coffee:cups VVVVVVVVVVVV Mass of the cups  water VVVVVVVVVVVV Mass of the cool water VVVVVVVVVVVV Temperature of water VVVVVVVVVVVV 3. Mass of unknown VVVVVVVVVVVV Temperature of boiling water VVVVVVVVVVVV 5. Time vs. temperature data;

=. 0alculate the specific heat of the unknown and identify it. Show workQ C s = VVVVVVVVVV 78gDo0 6dentity * VVVVVVVVVVVV -@3

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