L 5 -specific Heat - Copy.doc
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View L 5 -specific Heat - Copy.doc as PDF for free.
More details
- Words: 2,128
- Pages: 51
Physics 222L
Experiment 10
SPECIFIC HEAT AND LATENT HEAT OF FUSION Introduction: Heat, Q, is thermal energy transferred as a consequence of temperature differences. Internal energy, Eint, is the total thermal energy a substance has at some temperature T. The unit of heat most commonly used is the calorie (cal), now defined as 4.186 J. The heat Q required to change the temperature of a mass m of a given material by an amount T = Tf Ti is Q = C T = c m T
where the specific heat c for a given material is defined as the heat capacity C per unit mass. Specific heats for some common materials are given in your textbook. More extensive tables can be found in other references. A useful number is the specific heat for liquid water, 1.00 cal/gC. (Note that different phases of the same substance can have different specific heats. For example, the specific heat for ice near 0C is 0.53 cal/gC.) A change in internal energy is involved when a substance undergoes a change of phase; the heat Q required is Q = L m where m is the mass of material whose phase is changed and L, called the latent heat, depends on the nature of the phase change as well as on the properties of the substance. As a substance changes from a solid to a liquid phase, the heat required to effect this change for a unit mass of the substance is called its latent heat of fusion LF. The heat Q required to change mass m from solid to liquid is Q = LF m. As the substance changes from the liquid to the solid phase, it
releases an equal quantity of heat, i.e. Q = LF m. The latent heat of fusion of water, the heat required to change ice to liquid water at 0C, is 333kJ/kg = 79.5 cal/g. The first law of thermodynamics is a generalization of the law of conservation of energy to include heat and possible changes in internal energy. It states that the change in internal energy of a system, Eint = Eint,f Eint,i, is equal to the heat Q added to the system minus the work W done by the system: Eint = Eint,f Eint,i = Q W 101
In this experiment you will determine the specific heats of some samples of various materials by measuring their change in temperature when a measured amount of thermal energy is added. You will also measure the latent heat of fusion of water by determining how much thermal energy must be added to melt a measured mass of ice. No significant changes in mechanical energy will be involved; only exchanges of thermal energy among the parts of the system being studied will be considered. You will use a calorimeter, a device in which an inner system is isolated as well as possible from thermal energy transfers to or from the external environment. This inner system includes known or measured amounts of known substances as well as a sample of a substance x under study. The initial temperatures of the components of the inner system are known or measured. The components are allowed to exchange thermal energy and come to a common equilibrium temperature which is measured. For such a system, energy is conserved (to the extent that
exchanges with the environment can be neglected); the thermal energy gain by some parts of the system must equal the thermal energy loss by other parts. A single unknown (e.g. cx or mx) in the equation relating the thermal energy transfers can be determined. Equipment: Calorimeter with aluminum inner cup and aluminum stirrer, several metal samples including aluminum, copper, steel and brass, ice at 0C, laboratory balance, dial thermometer, tongs, beaker, water near room temperature, cold and hot tap water, facilities for heating samples. Procedure: A.
Specific Heat.
In this part of the experiment the inner calorimeter cup, the water in it, and the stirrer all gain thermal energy when a heated sample is placed within the cup. The sample loses thermal energy. First determine and record the room temperature. Note the material used for the calorimeter's inner cup and stirring device. Make sure the cup and stirrer are dry. Measure their masses and estimate the errors. Fill the inner cup about half full with water which is about 4 C colder than room temperature. (This is to minimize net thermal energy exchange with the surroundings. After adding the hot sample and allowing the system to come to equilibrium, the final equilibrium temperature should be a few C above room temperature.) Measure the mass of the cup plus water and estimate the error. Assemble the calorimeter, including the 102
thermometer, and stir the water so the whole inner assembly comes to equilibrium at a common temperature. Record this starting temperature and its estimated error. Take the calorimeter to the hot water bath. Record the temperature (with error) of the aluminum sample in the hot water bath and QUICKLY transfer the sample to the inner cup. Cover the calorimeter and observe the temperature changes as you stir the water. Record the equilibrium temperature and its error. (The temperature should rise rapidly as parts of the system exchange heat, then decrease slowly as heat is lost to the surroundings. The best estimate for the equilibrium temperature is the highest temperature reached.) Remove the sample from the cup and dry it off. Determine the mass of the (dry) sample and its error. After you are finished with the sample, carefully return it to the hot water bath. Repeat the process for two other samples of different materials. Among samples which may be available are copper, brass, and steel. (Do not use both copper and brass samples.) Note and record the nature of the samples you use. Values for the specific heats of the sample substances in cal/gC from various tables include: aluminum, 0.215; copper, 0.0923; brass, 0.089 to 0.092; and steel, 0.107 to 0.118. B.
Latent Heat of Fusion.
In this case the inner cup should initially contain water about 4 C above room temperature. (After adding ice and allowing the system to come to equilibrium, the final equilibrium temperature should be a few C below room temperature.) After determining the mass of water plus cup and its error, assemble the calorimeter, stir, and determine the initial temperature and its error. Then drop a sample of ice at 0C (Try not to add any liquid water at 0C.) into the calorimeter, stir, observe the temperature changes, and record the equilibrium temperature. As before, estimate the errors in all measured quantities. NOTE: Do not add too much i ce or you may end up with some ice still unmelted, the system at 0 C, and no way to calculate the latent heat. A 10 to 30 gram sample of ice is probably about right. After the temperature is measured, measure the final mass of water plus cup and its error. The difference between final mass and the starting mass determines the mass of ice which was added.
Analysis. In the calculations of this section, you may neglect any uncertainties in given values of specific heats and latent heats. If you check, you should find that the relative errors in the masses are much smaller than the relative errors in the temperature changes. If this is true, the errors in the masses may be neglected in the error calculations. A.
Specific Heat.
103
In each case, the thermal energy gain of the calorimeter cup c, water w, and stirrer s should equal the thermal energy loss of sample x as equilibrium is attained: Qx = Qw + Qc + Qs (The small contribution of the thermometer and any net heat exchanged with the environment will be neglected.) In terms of the masses, specific heats, and temperature changes this becomes: mx cx Tx = mw cw Tc + mc cc Tc + ms cs Tc where all of the mi and Ti can be determined from your measurements. The specific heat of liquid water cw is 1.00 cal/gC. The specific heats of the cup and stirrer are cc = cs = cAl. In the case of the aluminum sample, cx is also cAl which is the only undetermined quantity in the equation. Solve the equation for cAl. Substitute the values from your measurements and calculate a value for cAl. Use your error estimates and the rules of error propagation to calculate the error for your value. Is your measured value for the specific heat of aluminum consistent with the accepted value given below? Discuss (even if your measurement is consistent with this value) possible sources of error which have not been considered and which might contribute to any discrepancy. For the remainder of the experiment, use the accepted value, cAl = 0.215 cal/gC, for the specific heat of aluminum. For the other two samples used in your measurements, the only unknown in the equation is cx. Calculate values and the corresponding errors for cx for your other two samples using the results of your measurements. Consider the specific heats you determined for these other two samples. Are they consistent with the values listed in the Procedure section? B.
Latent Heat of Fusion.
In this case, the thermal energy gained by the ice in melting plus the thermal energy required to raise the temperature of the water from the melted ice to equilibrium should equal the thermal energy lost by the calorimeter and the water it initially contained.
or
Qmelting + Qice water = Qcalorimeter mice LF + mice cw Tice water = [ mw cw + mc cc + ms cs ]Tc
in terms of masses, specific heats, temperature changes, and LF, the latent heat of fusion for water. 104
Here Tice water is the temperature change of the water from the melted ice. Use the
accepted values for cw, cc, and cs. The only quantity not available from your measurements or from previous knowledge of specific heats is LF. Determine LF and its error using your measurements. Is your measured value for the latent heat of fusion of water consistent with the value given in the Introduction? Again, consider and discuss possible sources of error which may not have been considered in your error calculation.
Questions for the report: 1) Locate values in handbooks or other references for the specific heats of the materials of which the samples of part A were made. List the values you find and the sources from which they come. How do the values you found compare with the values given in these instructions and in your text. Compare your experimental values with values from your other sources. Discuss your findings. Can you think of any reasons why the values given in different references might differ? 2) Comment on the differences you would expect to observe in part B. if you added m grams of water at 0C instead of adding m grams of ice at 0C. 3) Comment on how the computed value of a specific heat in part A would be affected if you carried along some boiling water with the metal sample when you transferred it to the inner calorimeter cup. 4) Why would it not be practical to heat the metal samples to a much higher temperature in an oven so a greater change in the temperature of the water in the calorimeter would be produced?
NOTE: Before you leave the lab, you must have all the measurements and error estimates (for masses and temperatures) needed to calculate the specific heats for three samples and the latent heat of fusion of water. If possible, try some calculations before you leave to make sure that you have all required information and that your measurements seem reasonable. Make sure (as you always should for all measurements) that appropriate units have been listed for your measurements. Each lab partner must have a complete data sheet initialed by your TA. The rest of the work can be done outside of the laboratory.
105
Z Data on “Specific Heat & Latent Heat” Experiment
106
room
107
temperature
108
mass
109
of
cup
1010
=
1011
mass
1012
of
stirrer
1013
= error in temperature T = error in mass m =
A. Specific Heat for 3 Materials.
1014
sample
1015
x
1016
1017
1018
1019
1020
1021
1022
1023
1024
Al
B. Latent Heat for Ice Fusion
1025
mass
of
cup
1026
plus
water,
1027
=
1028
initial
temperature
1029
,
1030
ice
temperature
1031
,
1032
final
1033
temperature
1034
mass
of
cup
1035
+water
+ice,
1036
1037
1038
1039
1040
1041
=
1042
1043
1044
=
1045
1046
1047
=
1048
1049
1050
=
1051
Experiment 10
SPECIFIC HEAT AND LATENT HEAT OF FUSION Introduction: Heat, Q, is thermal energy transferred as a consequence of temperature differences. Internal energy, Eint, is the total thermal energy a substance has at some temperature T. The unit of heat most commonly used is the calorie (cal), now defined as 4.186 J. The heat Q required to change the temperature of a mass m of a given material by an amount T = Tf Ti is Q = C T = c m T
where the specific heat c for a given material is defined as the heat capacity C per unit mass. Specific heats for some common materials are given in your textbook. More extensive tables can be found in other references. A useful number is the specific heat for liquid water, 1.00 cal/gC. (Note that different phases of the same substance can have different specific heats. For example, the specific heat for ice near 0C is 0.53 cal/gC.) A change in internal energy is involved when a substance undergoes a change of phase; the heat Q required is Q = L m where m is the mass of material whose phase is changed and L, called the latent heat, depends on the nature of the phase change as well as on the properties of the substance. As a substance changes from a solid to a liquid phase, the heat required to effect this change for a unit mass of the substance is called its latent heat of fusion LF. The heat Q required to change mass m from solid to liquid is Q = LF m. As the substance changes from the liquid to the solid phase, it
releases an equal quantity of heat, i.e. Q = LF m. The latent heat of fusion of water, the heat required to change ice to liquid water at 0C, is 333kJ/kg = 79.5 cal/g. The first law of thermodynamics is a generalization of the law of conservation of energy to include heat and possible changes in internal energy. It states that the change in internal energy of a system, Eint = Eint,f Eint,i, is equal to the heat Q added to the system minus the work W done by the system: Eint = Eint,f Eint,i = Q W 101
In this experiment you will determine the specific heats of some samples of various materials by measuring their change in temperature when a measured amount of thermal energy is added. You will also measure the latent heat of fusion of water by determining how much thermal energy must be added to melt a measured mass of ice. No significant changes in mechanical energy will be involved; only exchanges of thermal energy among the parts of the system being studied will be considered. You will use a calorimeter, a device in which an inner system is isolated as well as possible from thermal energy transfers to or from the external environment. This inner system includes known or measured amounts of known substances as well as a sample of a substance x under study. The initial temperatures of the components of the inner system are known or measured. The components are allowed to exchange thermal energy and come to a common equilibrium temperature which is measured. For such a system, energy is conserved (to the extent that
exchanges with the environment can be neglected); the thermal energy gain by some parts of the system must equal the thermal energy loss by other parts. A single unknown (e.g. cx or mx) in the equation relating the thermal energy transfers can be determined. Equipment: Calorimeter with aluminum inner cup and aluminum stirrer, several metal samples including aluminum, copper, steel and brass, ice at 0C, laboratory balance, dial thermometer, tongs, beaker, water near room temperature, cold and hot tap water, facilities for heating samples. Procedure: A.
Specific Heat.
In this part of the experiment the inner calorimeter cup, the water in it, and the stirrer all gain thermal energy when a heated sample is placed within the cup. The sample loses thermal energy. First determine and record the room temperature. Note the material used for the calorimeter's inner cup and stirring device. Make sure the cup and stirrer are dry. Measure their masses and estimate the errors. Fill the inner cup about half full with water which is about 4 C colder than room temperature. (This is to minimize net thermal energy exchange with the surroundings. After adding the hot sample and allowing the system to come to equilibrium, the final equilibrium temperature should be a few C above room temperature.) Measure the mass of the cup plus water and estimate the error. Assemble the calorimeter, including the 102
thermometer, and stir the water so the whole inner assembly comes to equilibrium at a common temperature. Record this starting temperature and its estimated error. Take the calorimeter to the hot water bath. Record the temperature (with error) of the aluminum sample in the hot water bath and QUICKLY transfer the sample to the inner cup. Cover the calorimeter and observe the temperature changes as you stir the water. Record the equilibrium temperature and its error. (The temperature should rise rapidly as parts of the system exchange heat, then decrease slowly as heat is lost to the surroundings. The best estimate for the equilibrium temperature is the highest temperature reached.) Remove the sample from the cup and dry it off. Determine the mass of the (dry) sample and its error. After you are finished with the sample, carefully return it to the hot water bath. Repeat the process for two other samples of different materials. Among samples which may be available are copper, brass, and steel. (Do not use both copper and brass samples.) Note and record the nature of the samples you use. Values for the specific heats of the sample substances in cal/gC from various tables include: aluminum, 0.215; copper, 0.0923; brass, 0.089 to 0.092; and steel, 0.107 to 0.118. B.
Latent Heat of Fusion.
In this case the inner cup should initially contain water about 4 C above room temperature. (After adding ice and allowing the system to come to equilibrium, the final equilibrium temperature should be a few C below room temperature.) After determining the mass of water plus cup and its error, assemble the calorimeter, stir, and determine the initial temperature and its error. Then drop a sample of ice at 0C (Try not to add any liquid water at 0C.) into the calorimeter, stir, observe the temperature changes, and record the equilibrium temperature. As before, estimate the errors in all measured quantities. NOTE: Do not add too much i ce or you may end up with some ice still unmelted, the system at 0 C, and no way to calculate the latent heat. A 10 to 30 gram sample of ice is probably about right. After the temperature is measured, measure the final mass of water plus cup and its error. The difference between final mass and the starting mass determines the mass of ice which was added.
Analysis. In the calculations of this section, you may neglect any uncertainties in given values of specific heats and latent heats. If you check, you should find that the relative errors in the masses are much smaller than the relative errors in the temperature changes. If this is true, the errors in the masses may be neglected in the error calculations. A.
Specific Heat.
103
In each case, the thermal energy gain of the calorimeter cup c, water w, and stirrer s should equal the thermal energy loss of sample x as equilibrium is attained: Qx = Qw + Qc + Qs (The small contribution of the thermometer and any net heat exchanged with the environment will be neglected.) In terms of the masses, specific heats, and temperature changes this becomes: mx cx Tx = mw cw Tc + mc cc Tc + ms cs Tc where all of the mi and Ti can be determined from your measurements. The specific heat of liquid water cw is 1.00 cal/gC. The specific heats of the cup and stirrer are cc = cs = cAl. In the case of the aluminum sample, cx is also cAl which is the only undetermined quantity in the equation. Solve the equation for cAl. Substitute the values from your measurements and calculate a value for cAl. Use your error estimates and the rules of error propagation to calculate the error for your value. Is your measured value for the specific heat of aluminum consistent with the accepted value given below? Discuss (even if your measurement is consistent with this value) possible sources of error which have not been considered and which might contribute to any discrepancy. For the remainder of the experiment, use the accepted value, cAl = 0.215 cal/gC, for the specific heat of aluminum. For the other two samples used in your measurements, the only unknown in the equation is cx. Calculate values and the corresponding errors for cx for your other two samples using the results of your measurements. Consider the specific heats you determined for these other two samples. Are they consistent with the values listed in the Procedure section? B.
Latent Heat of Fusion.
In this case, the thermal energy gained by the ice in melting plus the thermal energy required to raise the temperature of the water from the melted ice to equilibrium should equal the thermal energy lost by the calorimeter and the water it initially contained.
or
Qmelting + Qice water = Qcalorimeter mice LF + mice cw Tice water = [ mw cw + mc cc + ms cs ]Tc
in terms of masses, specific heats, temperature changes, and LF, the latent heat of fusion for water. 104
Here Tice water is the temperature change of the water from the melted ice. Use the
accepted values for cw, cc, and cs. The only quantity not available from your measurements or from previous knowledge of specific heats is LF. Determine LF and its error using your measurements. Is your measured value for the latent heat of fusion of water consistent with the value given in the Introduction? Again, consider and discuss possible sources of error which may not have been considered in your error calculation.
Questions for the report: 1) Locate values in handbooks or other references for the specific heats of the materials of which the samples of part A were made. List the values you find and the sources from which they come. How do the values you found compare with the values given in these instructions and in your text. Compare your experimental values with values from your other sources. Discuss your findings. Can you think of any reasons why the values given in different references might differ? 2) Comment on the differences you would expect to observe in part B. if you added m grams of water at 0C instead of adding m grams of ice at 0C. 3) Comment on how the computed value of a specific heat in part A would be affected if you carried along some boiling water with the metal sample when you transferred it to the inner calorimeter cup. 4) Why would it not be practical to heat the metal samples to a much higher temperature in an oven so a greater change in the temperature of the water in the calorimeter would be produced?
NOTE: Before you leave the lab, you must have all the measurements and error estimates (for masses and temperatures) needed to calculate the specific heats for three samples and the latent heat of fusion of water. If possible, try some calculations before you leave to make sure that you have all required information and that your measurements seem reasonable. Make sure (as you always should for all measurements) that appropriate units have been listed for your measurements. Each lab partner must have a complete data sheet initialed by your TA. The rest of the work can be done outside of the laboratory.
105
Z Data on “Specific Heat & Latent Heat” Experiment
106
room
107
temperature
108
mass
109
of
cup
1010
=
1011
mass
1012
of
stirrer
1013
= error in temperature T = error in mass m =
A. Specific Heat for 3 Materials.
1014
sample
1015
x
1016
1017
1018
1019
1020
1021
1022
1023
1024
Al
B. Latent Heat for Ice Fusion
1025
mass
of
cup
1026
plus
water,
1027
=
1028
initial
temperature
1029
,
1030
ice
temperature
1031
,
1032
final
1033
temperature
1034
mass
of
cup
1035
+water
+ice,
1036
1037
1038
1039
1040
1041
=
1042
1043
1044
=
1045
1046
1047
=
1048
1049
1050
=
1051
Related Documents
L 5 -specific Heat - Copy.doc
April 2020 0
Understanding Specific Latent Heat
June 2020 3
Understanding Specific Heat Capacity
May 2020 0
Specific Heat Capacities Of An Ideal Gas
June 2020 3
Heat Lab 5.docx
November 2019 5