08 Specific Heat Capacity

45

Specific Heat Capacity PRE-LAB ASSIGNMENTS :

To be assigned by your lab instructor.

STUDENT LEARNING OUTCOMES: • • • • • • •

The First Law of Thermodynamics Thermal energy as a function of temperature The units of energy Sign conventions in heat flow Heat capacity Specific heat capacity Factors in experimental error

EXPERIMENTAL GOALS:

You will will measur measuree the specific specific heat capacity capacity of a known known metal. metal. Then Then you you will will measur measuree the specific heat capacity of an unknown to identify the metal.

INTRODUCTION : Heat Capacity

 large large part part of chemis chemistry try is studyi studying ng and underst understandi anding ng the physic physical al and chemic chemical al changes that matter matter undergoes. undergoes. The driving driving force for most chemical and physical physical changes is energy energy! often in the form of thermal energy energy "heat#. "heat#. Temper Temperature ature and heat are not the same $uanti $uantity ty.. The temper temperatu ature re of an ob%ect is an indica indicator tor of the amount amount of therma thermall energy energy it &possesses'! but heat is a measure of the transfer of energy to or from an ob%ect. (e know that the more a substance substance is heated! the more its temperature temperature will rise. This relations relationship hip is a direct direct proportionality that may be expressed as q ∝ ∆T ! where $ is the heat absorbed or released by the system and system and )T is its temperature change ")T *T final + Tinitial#. This proportionality proportionality may be also be written as an e$uality! q ∆T

=

constant

or

q

=

constant ⋅ ∆T

,-

The constant of proportionality is the heat capacity ! C ! and is defined as the $uantity of heat re$uired re$uired to change an ob%ect/s ob%ect/s temperature temperature by one unit of temperatur temperaturee "usually "usually - o0 or - 1#. Hence we can rewrite 2$uation - as q

=

C ⋅ ∆T

,3

4=

6t follows that heat capacity has units related to J o

C

energy temperatur e

and is commonly expressed as

"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
100 g

C * $

200 g

C' * 3$

Fi!"e #$ Heat re$uired for - o0 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 -o0 "see Figure 3#.

35.@°0 - g H3?

=.->= 7

33.@°0

4A Fi!"e &$ Specific heat capacity.

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

=

m ⋅ C s

⋅ ∆T

,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 C s

=

C -@@ g

=

C B 3@@ g

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 energy mass ⋅ temperatur e

. The units of specific heat are commonly expressed as

J g ⋅ o C

"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
,=

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 $uantity. n ideal calorimeter would provide perfect insulation so that its contents! the system! could undergo its temperature change without any loss or gain of heat to the surroundings or to the calorimeter itself. Such a calorimeter does not exist. 6nstead! we must build an apparatus that gains "or loses# a minimum amount of heat energy itself while also minimi
4J insulator. However! the heat lost by the system to the calorimeter is small! but not negligible! and it must be considered. (ith this correction! 2$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#

,

$cal * :"$lost by hot  $gained by cold #

,J

Iearrangement yields

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. Specific Heat Specific Heat Capacity) C s Capacity) C s . Meta( *+, C/ Meta( *+, .C/ Lead @.-34 0obalt @.=3Kold @.-34 ickel @.=== Tungsten @.-53 6ron @.==4 Elatinum @.-55 0hromium @.=A@ eodymium @.-4Manganese @.=J4 Tin @.33> Titanium @.A33 Silver @.35A Eotassium @.JAJ Strontium @.5@ luminum @.>4J 0opper @.5>A Magnesium -.@3 Ninc @.5>> Sodium -.35

4> SAMPLE CALCULATION

OF THE CALIBRATION OF A CALORIMETER :

(ater with a mass of A@.@ g at >@.- o0 was added to A@.@ g of water at 3J.3 o0. Gpon mixing! the final temperature attained was A-.4 o0. (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 78gDo0#D"A-.4 o0 + >@.- o0# * :A>4@ 7 Heat gained by cool water; $gained * "A@.@ g#D"=.-> 78gDo0#D"A-.4 o0 + 3J.3 o0# * A-@ 7 Heat absorbed by calorimeter; $cal * :":A>4@ 7  A-@ 7# * J5@ 7 Heat capacity of calorimeter; C cal

=

J5@ 7

(A-.4



0 − 3J.3 0) 

=

34 78o0

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 @.- o0. 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
44 =. 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 @.- o0. Transfer the thermometer to the calorimeter! and allow it to come to the same temperature that was recorded earlier.

split stopper

clamp

thermometer

stirrer lid

A. Quickly transfer the hot metal in the test tube to the calorimeter containing the water. 3 nested Styrofoam cups 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 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

U error

=

* Tf : Ti

"your value : true value# true value

×

-@@

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.

-@@ LAB R EPORT Specific Heat Capacity

ame

VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV

Eartner VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV

Wate VVVVVVVVV

Ieport Krade VVVVVV

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#

@

-@A

3-@

-A

-3@

33A

5@

-5A

3=@

=A

-A@

3AA

@

-A

3J@

JA

->@

3>A

4@

-4A

5@@

Maximum System Temperature "Tf #

Temperature "90#

VVVVVVVVVVVV

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

U error * VVVVVVVVVVVV

-@-

A. Mass of the coffee:cups

VVVVVVVVVVVV


VVVVVVVVVVVV

Mass of the water

VVVVVVVVVVVV

Temperature of cool water

VVVVVVVVVVVV

. 6dentity of metal sample

VVVVVVVVVVVV

Mass of metal sample

VVVVVVVVVVVV


VVVVVVVVVVVV

J. Time vs. temperature data + second run; Time "sec#

Temperature "90#

Time "sec#

Temperature "90#

Time "sec#

@

-@A

3-@

-A

-3@

33A

5@

-5A

3=@

=A

-A@

3AA

@

-A

3J@

JA

->@

3>A

4@

-4A

5@@


Temperature "90#

VVVVVVVVVVVV

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


4. verage specific heat of the known and percent error . C s = VVVVVVVVVV 78gDo0


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

-. Gnknown umber

VVVVVVVVVVVV

Mass of the coffee:cups

VVVVVVVVVVVV


VVVVVVVVVVVV

Mass of the cool water

VVVVVVVVVVVV

Temperature of water

VVVVVVVVVVVV

3. Mass of unknown

VVVVVVVVVVVV


VVVVVVVVVVVV

5. Time vs. temperature data; Time "sec#

Temperature "90#

Time "sec#

Temperature "90#

Time "sec#

@

-@A

3-@

-A

-3@

33A

5@

-5A

3=@

=A

-A@

3AA

@

-A

3J@

JA

->@

3>A

4@

-4A

5@@


Temperature "90#

VVVVVVVVVVVV

=. 0alculate the specific heat of the unknown and identify it. Show workQ C s = VVVVVVVVVV 78gDo0

6dentity * VVVVVVVVVVVV

-@5

08 Specific Heat Capacity

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