23. Specific Heat Capacity of a Metal



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23. Specific Heat Capacity of a Metal

Objectives

In this experiment, students compare the heat transferred by different metals to water. By comparing the heat transfer, students learn:



  • How different metals store heat

  • That the capacity of a substance to store heat is a characteristic of that substance

Procedural Overview

Students gain experience conducting the following procedures:



  • Measuring the temperature change caused by introducing a higher temperature metal to a room temperature liquid

  • Thermally isolating metal and liquid samples to insure that the heat transfer is only between samples

  • Comparing the heat transferred by different metals to determine the heat capacities of the metals

Time Requirement

  • Preparation time

10 minutes

  • Pre-lab discussion and activity

10 minutes

  • Lab activity

35 minutes

Materials and Equipment

For each student or group:

  • Data collection system

  • Balance (1 per classroom)

  • Temperature sensor, stainless steel

  • Hot plate

  • Beaker, 600-mL

  • Tongs

  • Calorimetry cup (3)1

  • Water, 1 L

  • Metal sample (3)1

  • String, 15-cm (3)

1 Part of the Basic Calorimetry Set

Concepts Students Should Already Know

Students should be familiar with the following concepts:



  • Heat as energy

  • Heat transfer

Related Labs in This Guide

Labs conceptually related to this one include:



  • Temperature versus Heat

  • Phase Change

  • Heat of Fusion

  • Heat of Vaporization

Using Your Data Collection System

Students use the following technical procedures in this activity. The instructions for them (identified by the number following the symbol: "") are on the storage device that accompanies this manual. Choose the file that corresponds to your PASCO data collection system. Please make copies of these instructions available for your students.



  • Starting a new experiment on the data collection system (1.2)

  • Connecting a sensor to the data collection system (2.1)

  • Starting and stopping data recording (6.2)

  • Displaying data in a graph (7.1.1)

  • Adjusting the scale of a graph (7.1.2)

  • Finding the values of a point in a graph (9.1)

  • Saving your experiment (11.1)

Background

Doing work can add energy to systems or a substance. Examples include pushing a cart up an inclined track or using a wrench to tighten a bolt. However, this is not the only way to introduce energy to a system or substance. Energy can be added in the form of heat Q. Unlike work energy, energy added by heat has the ability to cause changes in the substance itself, such as changes in temperature and changes in phase.

One can experience an example of this heat (energy) exchange by dropping a cold metal spoon into a pot of hot water. After remaining in the water for a few minutes, the spoon feels hot when removed. When the spoon entered the hot water, the spoon began to absorb energy and convert that energy gain into a change in temperature.

One may have also noticed that after removing the spoon, the temperature of the water dropped slightly. This is a result of energy conservation within the system: as the cold spoon's energy (temperature) increases, the hot water's energy (temperature) must decrease.

The spoon in this example was made out of metal. How would the temperature changes be different if the spoon were plastic? One would expect a cold metal spoon to cause a greater drop in the water temperature than a plastic spoon. However, this is a property of the specific heat capacity and mass of the object or substance. Specific heat is informally described as a substance's ability to resist changes in temperature due to the addition or subtraction of heat energy. Some substances require large amounts of energy to change just a slight amount in temperature, while others will change temperature with just a tiny bit of added energy.

The mathematical relationship between energy Q and temperature change ΔT for a substance of mass m is shown here:



Eq.1

where c is the specific heat capacity of the substance.

For positive temperature changes (Tfinal - Tinitial > 0), energy is added to a substance. When ΔT is negative, Q is also negative, which indicates that energy is leaving a substance. Because of energy conservation, we can relate the changes in temperature from one part of the system to the other using this simple relationship:

Eq.2

Eq.3

In the spoon example, the right side of Eq.3 corresponds to the energy gained by the spoon; the left corresponds to the energy lost by the hot water; and each has a mass mn and experiences a change in temperature ΔTn that is governed by their specific heats cn.



Pre-Lab Discussion and Activity

Engage your students with the following questions:

1. What do we know about heat at this point?

Heat is a form of energy. Heat flows from higher temperature objects to lower temperature objects through contact.

2. We have seen that heat flows from high temperature substances to low temperature substances. How do you think we can use this fact to find out more about how metals store and transfer heat.



Teacher Tip: Open up the topic to discussion, and collect ideas on a white board.

We can compare the characteristics of a known substance to those of an unknown. Direct the discussion toward the idea of heating the metal to a known temperature and placing them in a substance with a known heat characteristic, like water.

3. What parameters do you think we will need to hold constant, and which will we measure and compare?

Teacher Tip: Open up the topic to discussion, and collect ideas on a white board.

Things to remain constant: initial temperature of the metal, initial temperature of the water mass of the metal sample, and mass of the water. Things to measure and compare: final temperature of the water and the rate of change of the temperature.



Lab Preparation

These are the materials and equipment to set up prior to the lab:

1. Place the water at the lab stations ahead of time to minimize spills.

2. Provide students with two known metal samples and one "unknown" sample.

Lab Safety

Add these important safety precautions to your normal laboratory procedures:


  • When using the hot plate, be very careful not to burn your hands or fingers.

  • Use a 600-mL beaker for boiling water that can withstand high heat, such as a Pyrex® beaker. Other beakers may shatter when exposed to high heat.

  • Boiling water can cause severe burns. Be very careful when using boiling water, and do not carry the beaker without insulated gloves or tongs when it is hot.

  • All glass beakers can break when dropped. Be very careful not to drop any of the glassware used in this lab. If an accident does occur, follow the proper cleaning and disposal procedure instituted by your teacher.

  • Keep electronic and other sensitive equipment away from water.

Sequencing Challenge

T
he steps below are part of the Procedure for this lab activity. They are not in the right order. Determine the proper order and write numbers in the circles that put the steps in the correct sequence.


Procedure with Inquiry

After you complete a step (or answer a question), place a check mark in the box () next to that step.

Note: Students use the following technical procedures in this activity. The instructions for them (identified by the number following the symbol: "") are on the storage device that accompanies this manual. Choose the file that corresponds to your PASCO data collection system. Please make copies of these instructions available for your students.

Set Up

1.  Start a new experiment on your data collection system. (1.2)

2.  Connect the temperature sensor to the data collection system. (2.1)

3.  Display Temperature on the y-axis of a graph with Time on the x-axis. (7.1.1)

4.  Create a hot water bath by filling the beaker ¾ full with water and placing the beaker on the hot plate.

5.  Set the hot plate temperature to boil the water in the beaker.

6.  Why is it better to use boiling water to heat the metal sample and not room temperature water?

Water boils at around 100 °C, so we already know the initial temperature, and it will stay constant as the metal heats up. (Boiling water generally doesn't get any hotter than 100 °C.) If we were to use room temperature water, the temperature would change when we introduced the metal.

7.  In this lab, we will use boiling water to heat the metal sample to ~100 °C. Could we have used ice water to cool the sample to ~0 °C so that the temperature of the calorimeter water would drop rather than increase? Explain.

Yes. The ice water would behave the same way the boiling water did by not changing temperature when we introduce the metal. We also know that the temperature should be 0 °C for ice water. The difference would be the direction of heat flow.

8.  Use the balance to measure the mass of the calorimetry cups, and then record the mass of the calorimeter cups in the Data Analysis section.

9.  Add equal amounts of water to the calorimetry cups (approximately ¾ full), and record the mass of the calorimeter with water in the Data Analysis section for each cup.



Note: The calorimeter and beaker are only ¾ full so that the water level does not spill over the edge up the cup when you submerge the metal sample.

10.  Why do we use a calorimetry cup when measuring the change in water temperature and not just another glass beaker?

The calorimeter is insulated and won't lose much energy (heat) through conduction through its walls. A glass beaker is not insulated and would allow heat to escape into the air.

11.  Record the mass of each metal sample in the Data Analysis section.

12.  Tie a 15-cm piece of string to each metal sample to make them easier to move from the hot water bath to the calorimeter cup.

Collect Data

13.  Start data recording. (6.2)

14.  Check the temperature in each calorimeter to insure it is room temperature, and record this value in the Data Analysis section as the initial temperature of the water in the calorimeters.

15.  Allow the hot water bath to come to a boil, and then use the temperature sensor to measure the temperature of the boiling water.

16.  Why do you think it is important to measure the temperature of the boiling water if we "know" that water boils at 100 °C?

Pressure (or altitude) affects the temperature at which water boils, so it is best to measure. The important factor is that the boiling point will be constant for the local conditions.

17.  Stop data recording. (6.2)

18.  Remove the temperature sensor from the hot water bath.

19.  Place the first sample in the hot water bath, and allow it to equilibrate for 5 to 10 minutes.

20.  Place the temperature sensor in the first calorimeter.

21.  Start data recording. (6.2)

22.  Quickly but carefully transfer the first metal sample from the hot water bath to the calorimeter.

23.  Place the second metal sample in the hot water bath.

24.  Once the temperature in the calorimeter reaches equilibrium (remains constant), stop data recording. (6.2)

25.  Use the graph of Temperature versus Time on your data collection system to find the value of the equilibrium temperature. Record the temperature as the final temperature of both the water and the metal sample in the Data Analysis
section. (9.1)

26.  Place the temperature sensor in the second calorimeter.

27.  Start data recording. (6.2)

28.  Quickly but carefully transfer the second metal sample from the hot water bath to the calorimeter.

29.  Place the third metal sample in the hot water bath.

30.  Once the temperature in the calorimeter reaches equilibrium (remains constant), stop data recording. (6.2)

31.  Use the graph of Temperature versus Time on your data collection system to find the value of the equilibrium temperature. Record the temperature as the final temperature of both the water and the metal sample in the Data Analysis
section. (9.1)

32.  Place the temperature sensor in the third calorimeter.

33.  Start data recording. (6.2)

34.  Quickly but carefully transfer the third metal sample from the hot water bath to the calorimeter.

35.  Once the temperature in the calorimeter reaches equilibrium, (remains constant) stop data recording. (6.2)

36.  Use the graph of Temperature versus Time on your data collection system to find the value of the equilibrium temperature. Record the temperature as the final temperature of both the water and the metal sample in the Data Analysis


section. (9.1)

37.  Save your experiment as instructed by your teacher. 11.1)

38.  Make sure your hot plate is turned off, and carefully clean-up as instructed by your teacher.

Data Analysis

1.  After recording temperature data for all three of your samples, calculate the change in temperature ΔT for both the calorimeter water and the metal sample. Then, use those values to calculate the specific heat c of the sample.

The Specific heat of water is cwater = 4,186 J/(kg·°C).

Mass of the calorimeter cup: 0.019 kg


Mass of the calorimeter cup plus water: 0.188 kg

Table 1: Mass and temperature data




Sample 1

Tfinal (°C)

Tinitial (°C)

ΔT (°C)

m (kg)

Q (J)

Calorimeter Water

29.0

23.3

5.7

0.169

4,032.4

Aluminum

29.0

98.5

-69.2

0.066





Mass of the calorimeter cup: 0.021 kg


Mass of the calorimeter cup plus water: 0.223 kg

Table 2: Mass and temperature data




Sample 2

Tfinal (°C)

Tinitial (°C)

ΔT (°C)

m (kg)

Q (J)

Calorimeter Water

33.0

27.5

5.5

0.202

4,719.7

Copper

33.0

98.2

-65.2

0.199





Mass of the calorimeter cup: 0.024 kg

Mass of the calorimeter cup plus water: 0.229 kg

Table 3: Mass and temperature data




Unknown Sample

Tfinal (°C)

Tinitial (°C)

ΔT (°C)

m (kg)

Q (J)

Calorimeter Water

25.8

23.4

2.4

0.205

2,059.5

Metal Sample

25.8

98.5

-72.7

0.229







Analysis Questions

1. What were your calculated values for the specific heat of your first two sample metals? How did they correspond to the theoretical values shown in the table below? What was your percent error for each?

Sample 1 (Aluminum):

Experimental: 882.9 J/(kg∙°C) Theoretical: 900 J/(kg∙°C)

%error = |900-882.9|/900 = 1.9%

Sample 2 (Copper):

Experimental: 363.8 J/(kg∙°C) Theoretical: 387 J/(kg·°C)

%error = |387-363.8|/387 = 6.0%

Table 3: Specific heat of different metals


Substance

Specific Heat J/(kg·°C)

Aluminum

900

Beryllium

1,830

Cadmium

230

Copper

387

Germanium

322

Gold

129

Iron

448

Lead

128

Silver

234

Brass

380

2. Using the table above, what kind of metal is your unknown sample?

Unknown Metal: Lead

Experimental: 123.7 J/(kg·°C)

The closest theoretical value would be Lead at 128 J/(kg·°C), meaning that the percent error is equal to: |128-123.7|/128 = 3.4%

3. Explain some of the factors that may have caused your calculated values for specific heat c to be inaccurate and how these factors may have been avoided.

When we placed the metal sample in the calorimeter cup, there were still hot droplets of water on the sample. These droplets may have added some energy at a different specific heat than the metal sample, which we did not include in our calculations. This is somewhat unavoidable because anything used to dry the sample will absorb energy when it touches the sample.

Energy was lost in the calorimeter cup even though it did insulate very well. We could have used a more industrial calorimeter that insulated better, but this wouldn't have made too much of a difference because it would heat up as well.

Energy was lost from the surface of the water into the air. We could have used a lid over the calorimeter to help insulate the surface of the water.

The temperature probe used had a stainless steel sleeve on it that may have absorbed or added energy to the system, which was not included in our calculation. We could have heated or cooled the probe in advance to help minimize the energy loss or transfer from the probe.

Synthesis Questions

Use available resources to help you answer the following questions.

1. If one places a 100 g hot piece of copper in a calorimeter containing 200 g of room temperature (25 °C) water, and the final equilibrium temperature of the water + copper was 75 °C, what was the initial temperature of the copper before it was placed in the calorimeter? Show your work.









2. If a piece of iron and a piece of gold (same mass) were both exposed to the same amount of heat (Assume 100 g samples with the addition of 1,200 J of energy), which one would be hotter? Explain.

The specific heat of gold is much smaller than iron, which means that gold is prone to temperature changes with the addition of little energy, compared to iron. Gold will be hotter.

Gold:

Iron:

3. Explain in terms of energy why wood is used to insulate homes rather than metal, considering that the specific heat of wood is ~1,800 J/(kg·°C).

Because wood has a much higher specific heat, it resists changes in temperature due to the addition of energy compared better than most metals.

Multiple Choice Questions

1. Which of the following metals requires the most energy to experience a temperature change of 20 °C?

A. Copper

B. Gold.


C. Lead

D. Silver

2. If 300 g of room temperature water (25 °C) is heated and experiences a temperature increase of 40 °C, how much energy has the water absorbed?

A. 75.2 kJ

B. 50.2 J

C. 80.7 J

D. 50.2 kJ

3. If the same water from the previous question was then heated again such that it experiences another temperature increase of 40 °C, how much more energy has the water absorbed?

A. 50.2 kJ

B. 75.2 kJ

C. 725.0 kJ

D. Cannot solve this with just Eq.1; water turns to steam at 100 °C.



Key Term Challenge

Fill in the blanks from the list of randomly ordered words in the Key Term Challenge Word Bank.

1. When energy is added to a substance in the form of heat, that substance experience a change in temperature. However, not all substances experience the same change in temperature from the same addition of energy. The magnitude of temperature change depends on that substance's specific heat capacity. A substance with a large specific heat has a tendency to resist temperature changes with the addition or subtraction of heat energy, while a substance with a small specific heat will easily increase in temperature with the addition of heat energy.

2. Energy is a conserved quantity, thus indicating that the total energy in a closed system is constant. If a closed system consisted of a hot piece of copper submerged in a pool of cold mercury, the energy lost by the piece of copper must equal the amount of energy gained by the mercury. The mercury's temperature would increase while the copper's temperature would decrease relative to the specific heat and mass of each substance.

Extended Inquiry Suggestions

A natural extension to this activity is to ask your students to go back to their data and look at the first thirty seconds of the Temperature versus Time graph for each metal. Ask your students to compare the slope of a best fit line for each metal sample. Discuss the factors that might influence the rate at which heat transfers.







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