4. Calorimetry

Calorimetry

What Is Calorimetry?

Calorimetry is the measurement of energy transferred as heat during physical or chemical processes.

A device used to make these measurements is called a calorimeter.

Calorimetry can be used to investigate:

• specific heat capacities
• energy released by fuels
• energy contained in foods
• energy changes during chemical reactions
• final temperatures when substances are mixed
• latent heat during phase changes

The central idea is the conservation of energy:

Energy cannot be created or destroyed; it can only be transferred or transformed.

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Energy Conservation in Calorimetry

Consider a hot metal block placed into cooler water.

Thermal energy flows:

hot metal → cooler water

The metal loses energy while the water gains energy.

In an ideal insulated system:

energy lost by hot object = energy gained by cold object

This relationship forms the basis of many calorimetry calculations.

Another useful way to express this is:

Q_lost + Q_gained = 0

when signs are included.

In many school calculations, however, we simply equate the magnitudes:

Q_lost = Q_gained

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Reaching Thermal Equilibrium

When two objects at different temperatures are placed in thermal contact, energy transfers from the warmer object to the cooler object.

Eventually they reach the same temperature.

This condition is called thermal equilibrium.

For example:

hot metal + cool water → common final temperature

At thermal equilibrium, there is no longer any net heat transfer between them.

The final temperature should lie between the two initial temperatures if there are no additional energy sources or phase changes.

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The Main Calorimetry Equation

When a substance changes temperature without changing state, the energy transferred is:

Q = mcΔT

where:

• Q = energy transferred, in J
• m = mass, in kg
• c = specific heat capacity, in J/(kg·°C)
• ΔT = temperature change, in °C or K

Remember:

ΔT = T_final − T_initial

When comparing energy lost and gained, it is often easier to use the magnitude of each temperature change.

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A Simple Mixing Experiment

Suppose hot water is mixed with cold water inside an insulated container.

The hot water transfers energy to the cold water.

Ideally:

energy lost by hot water = energy gained by cold water

Using Q = mcΔT:

m_hot c_hot ΔT_hot = m_cold c_cold ΔT_cold

If both samples are water, their specific heat capacities are equal and can cancel:

m_hot ΔT_hot = m_cold ΔT_cold

This makes the final temperature relatively easy to calculate.

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Worked Example: Mixing Water

100 g of water at 80°C is mixed with 200 g of water at 20°C.

Assume no energy is transferred to the surroundings or container.

Let the final temperature be T_f.

Because both substances are water:

energy lost by hot water = energy gained by cold water

Convert masses:

100 g = 0.100 kg

200 g = 0.200 kg

Set up the equation:

0.100c(80 − T_f) = 0.200c(T_f − 20)

The c values cancel:

0.100(80 − T_f) = 0.200(T_f − 20)

Expand:

8 − 0.1T_f = 0.2T_f − 4

12 = 0.3T_f

T_f = 40°C

Therefore, the final equilibrium temperature is:

40°C

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Checking the Answer

A useful check is to compare the calculated final temperature with the initial temperatures.

Initially:

hot water = 80°C

cold water = 20°C

Calculated:

final temperature = 40°C

Since:

20°C < 40°C < 80°C

the answer is physically reasonable.

If the calculation had produced 100°C or −10°C, something would probably be wrong under the stated assumptions.

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Different Materials

Calorimetry becomes more interesting when different substances are involved.

Suppose a hot metal block is placed in cooler water.

Because metal and water have different specific heat capacities, we use:

m_metal c_metal ΔT_metal = m_water c_water ΔT_water

If the metal's specific heat capacity is unknown, the equation can be rearranged to determine it.

This is a common laboratory method for measuring specific heat capacity.

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Measuring the Specific Heat Capacity of a Metal

A typical experiment involves:

1. measuring the mass of a metal sample
2. heating the metal to a known temperature
3. measuring the mass and initial temperature of water
4. quickly placing the hot metal into the water
5. insulating the container
6. measuring the final equilibrium temperature

The energy lost by the metal is assumed to equal the energy gained by the water.

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Worked Example: Finding Specific Heat Capacity

A 0.20 kg metal block at 100°C is placed into 0.50 kg of water at 20°C.

The final temperature is 25°C.

For water:

c_water = 4200 J/(kg·°C)

First calculate the energy gained by the water.

ΔT_water = 25 − 20

ΔT_water = 5°C

Use:

Q = mcΔT

Q_water = 0.50 × 4200 × 5

Q_water = 10,500 J

Assuming no energy is lost:

Q_metal = 10,500 J

The metal cools from 100°C to 25°C:

ΔT_metal = 100 − 25

ΔT_metal = 75°C

Now:

10,500 = 0.20 × c_metal × 75

10,500 = 15c_metal

c_metal = 700 J/(kg·°C)

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Calorimeters

A good calorimeter attempts to minimize unwanted energy transfer between the experiment and the surroundings.

Simple calorimeters may use:

• insulated foam cups
• lids
• thermometers
• temperature probes
• insulating material

More advanced calorimeters use carefully controlled and highly insulated systems.

No real calorimeter is perfectly insulated, so experimental results always contain some uncertainty.

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Why Foam Cups Are Useful

Foam contains many small pockets of trapped gas.

Both the foam and trapped gas are poor thermal conductors.

The small pockets also restrict convection.

Therefore, a foam cup reduces energy transfer between the contents and surroundings.

A lid further reduces:

• convection
• evaporation
• exchange of warm or cool air

This helps the experiment behave more like an isolated thermal system.

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Calorimetry and Chemical Reactions

Calorimetry can also measure energy changes during chemical reactions.

Suppose two solutions react inside an insulated cup.

If the reaction releases energy:

chemical energy → thermal energy

The temperature of the solution rises.

If the reaction absorbs energy from the surroundings, the temperature may decrease.

By measuring the temperature change, the energy transferred to or from the solution can be estimated.

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Exothermic Reactions

An exothermic reaction transfers energy to the surroundings.

In a simple calorimeter:

reaction releases energy → solution gains energy → temperature rises

Examples can include:

• combustion
• some neutralization reactions
• some oxidation reactions

The energy gained by the solution can be estimated using:

Q = mcΔT

where m and c refer to the solution being heated.

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Endothermic Reactions

An endothermic reaction absorbs energy from the surroundings.

In a calorimeter:

reaction absorbs energy → solution loses thermal energy → temperature decreases

Some dissolving processes and chemical reactions are endothermic.

Calorimetry can therefore help determine whether a process releases or absorbs energy.

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Measuring Energy in Food

Food contains chemical energy.

A simple experiment can estimate the energy released when food burns.

The food is burned underneath a known mass of water.

Energy released by the food is transferred to the water.

The water's temperature increase is measured.

Then:

Q_water = m_water c_water ΔT

This provides an estimate of the energy transferred from the burning food.

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Worked Example: Food Calorimetry

A burning food sample heats 0.20 kg of water from 20°C to 45°C.

For water:

c = 4200 J/(kg·°C)

First:

ΔT = 45 − 20

ΔT = 25°C

Then:

Q = mcΔT

Q = 0.20 × 4200 × 25

Q = 21,000 J

Therefore, the water gained:

21,000 J

or:

21 kJ

If the food sample lost 0.50 g of mass while burning, the measured energy released per gram would be:

21 kJ ÷ 0.50 g = 42 kJ/g

However, this simple experiment usually underestimates the actual energy content of the food.

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Why Simple Food Calorimetry Is Inaccurate

Not all the energy released by the burning food reaches the water.

Energy can be transferred to:

• surrounding air
• the container
• the thermometer
• the clamp and equipment
• nearby surfaces

The food may also undergo incomplete combustion.

As a result:

energy measured by water < total energy released by food

A simple classroom food calorimeter therefore usually produces a value lower than the accepted energy content.

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Bomb Calorimeters

A bomb calorimeter is a more sophisticated instrument used to measure energy released during combustion.

The sample burns in a sealed chamber surrounded by water.

The system is carefully insulated.

Bomb calorimeters provide more accurate measurements because:

• combustion can be more complete
• energy transfer is more carefully controlled
• the calorimeter itself can be calibrated
• heat losses are minimized

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Calorimetry and Phase Changes

Calorimetry can also involve phase changes.

If ice is placed into warm water, energy transfers from the water to the ice.

Some energy may:

1. warm the ice to its melting point
2. melt the ice
3. warm the resulting liquid water

Different equations may therefore be required.

For temperature changes:

Q = mcΔT

For phase changes:

Q = mL

Energy conservation still applies:

total energy lost = total energy gained

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Example: Ice in Warm Water

Suppose ice at 0°C is placed into warm water.

The warm water cools.

The ice absorbs energy and melts.

If all the ice melts:

energy lost by warm water = energy used to melt ice + energy used to warm melted ice

This might require:

Q_water = Q_melting + Q_warming

or:

m_water c_water ΔT = m_ice L_f + m_ice c_water ΔT

Calorimetry problems can therefore combine specific heat capacity and latent heat.

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Finding an Unknown Final Temperature

Many calorimetry problems ask for the final equilibrium temperature.

The general strategy is:

Step 1: Identify which object loses energy.

Step 2: Identify which object gains energy.

Step 3: Write an energy equation.

Step 4: Substitute Q = mcΔT where appropriate.

Step 5: Solve for the unknown final temperature.

Step 6: Check that the answer is physically reasonable.

A useful starting equation is:

energy lost = energy gained

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Sources of Experimental Error

Real calorimetry experiments are not perfectly isolated.

Several sources of error can affect the results.

Energy Transfer to the Surroundings

Energy may escape through:

• conduction
• convection
• radiation

Better insulation reduces these losses.

Energy Absorbed by the Calorimeter

The cup, thermometer and other equipment also absorb energy.

Ignoring this can produce inaccurate results.

Evaporation

Evaporation removes energy from liquids and may change their mass.

A lid can reduce this effect.

Temperature Measurement

Possible problems include:

• thermometer uncertainty
• slow sensor response
• incorrect reading
• measuring before equilibrium is reached

Incomplete Mixing

Different regions of a liquid may have different temperatures.

Stirring gently helps produce a more uniform temperature.

Delays

Energy may be lost while transferring a heated object into the calorimeter.

Performing the transfer quickly reduces this problem.

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Improving a Calorimetry Experiment

Accuracy can be improved by:

• using better insulation
• using a lid
• transferring samples quickly
• stirring consistently
• using accurate temperature probes
• recording temperature continuously
• accounting for the heat capacity of the calorimeter
• reducing evaporation
• repeating measurements
• averaging reliable trials

A good experimental design attempts to make the real system behave as closely as possible to the ideal model used in the calculations.

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Calorimeter Heat Capacity

In more accurate experiments, the calorimeter itself cannot be ignored.

The calorimeter may gain or lose energy according to:

Q_cal = C_calΔT

where:

• Q_cal = energy transferred to the calorimeter
• C_cal = heat capacity of the calorimeter, in J/°C
• ΔT = temperature change

The energy equation might then become:

Q_hot = Q_cold + Q_cal

This produces a more realistic model.

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Interpreting Experimental Results

Calorimetry results should not simply be accepted without evaluation.

Suppose the accepted specific heat capacity of a material is:

900 J/(kg·°C)

but an experiment gives:

760 J/(kg·°C)

The difference suggests that the assumptions of the experiment were not completely satisfied.

Possible explanations include:

• energy lost to the surroundings
• inaccurate temperature measurements
• inaccurate mass measurements
• energy absorbed by equipment
• insufficient time to reach equilibrium

Scientists should consider both the calculated value and the quality of the experimental evidence.

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Percentage Error

Experimental values can be compared with accepted values using percentage error:

percentage error = |experimental − accepted| / accepted × 100%

For example:

experimental value = 760 J/(kg·°C)

accepted value = 900 J/(kg·°C)

Difference:

|760 − 900| = 140

Percentage error:

140/900 × 100%

≈ 15.6%

This provides a useful measure of how far the experimental result is from the accepted value.

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Practical Applications of Calorimetry

Calorimetry is used in many scientific and technological fields.

Food Science

Determining the energy released by foods.

Chemistry

Measuring energy changes during reactions.

Materials Science

Determining specific heat capacities and thermal properties.

Engineering

Evaluating heating, cooling and energy-storage systems.

Environmental Science

Studying thermal properties of materials and systems.

Fuel Testing

Comparing the energy released by different fuels.

Calorimetry therefore connects thermal physics with chemistry, biology, engineering and environmental science.

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Common Mistakes

Mistake: "The hot object loses temperature."
An object loses energy. Its temperature decreases as a result.

Mistake: "Energy lost and gained are always exactly equal in a real experiment."
Total energy is conserved, but some may transfer to the container or surroundings rather than the object being measured.

Mistake: "The final temperature can be higher than both starting temperatures."
For simple mixing without an additional energy source or reaction, the equilibrium temperature should lie between the initial temperatures.

Mistake: "Use grams directly in Q = mcΔT."
If c is given in J/(kg·°C), convert mass to kilograms.

Mistake: "The calorimeter does not absorb energy."
Real calorimeters have heat capacity and may need to be included in accurate calculations.

Mistake: "A result different from the accepted value means the experiment failed."
Experimental differences can provide useful information about uncertainty, heat loss and limitations in the procedure.

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Key Terms

Calorimetry — measurement of energy transferred as heat during physical or chemical processes.

Calorimeter — device used to measure thermal energy transfers.

Conservation of energy — principle stating that energy cannot be created or destroyed, only transferred or transformed.

Thermal equilibrium — state in which objects have the same temperature and there is no net heat transfer between them.

Specific heat capacity — energy required to raise the temperature of 1 kg of a substance by 1°C or 1 K.

Heat capacity — energy required to raise the temperature of an entire object by 1°C or 1 K.

Exothermic — describing a process that transfers energy to the surroundings.

Endothermic — describing a process that absorbs energy from the surroundings.

Latent heat — energy transferred during a phase change without a temperature change.

Experimental error — difference between an experimental result and the accepted or actual value resulting from limitations in measurement or method.

Percentage error — comparison between experimental and accepted values expressed as a percentage.

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Key Takeaways

• Calorimetry measures energy transfers in thermal systems.
• Calorimetry is based on the conservation of energy.
• In an ideal insulated system, energy lost = energy gained.
• Objects exchanging energy eventually reach thermal equilibrium.
• For temperature changes, use Q = mcΔT.
• For phase changes, use Q = mL.
• Calorimetry can determine unknown temperatures, specific heat capacities and energy transfers.
• Chemical reactions can be studied by measuring the temperature changes they produce.
• Food calorimetry estimates the chemical energy released by food.
• Real calorimeters are not perfectly isolated.
• Energy transferred to the container and surroundings can affect experimental results.
• Insulation, lids, rapid transfer and accurate temperature measurements improve calorimetry experiments.
• More accurate calculations may include the heat capacity of the calorimeter itself.
• Calorimetry has applications in physics, chemistry, food science and engineering.

Check Your Understanding

1. What is the purpose of calorimetry?
2. Explain how conservation of energy is used in a calorimetry experiment.
3. A hot metal block is placed into cooler water. Which object gains energy and which loses energy?
4. Why should the final equilibrium temperature normally lie between the two initial temperatures?
5. Calculate the energy required to heat 0.50 kg of water from 20°C to 35°C. Use c = 4200 J/(kg·°C).
6. A hot object loses 12,000 J in an ideal calorimeter. How much energy does the cooler substance gain?
7. Explain why foam cups are often used in simple calorimetry experiments.
8. Why can ignoring the calorimeter's own heat capacity introduce error?
9. A food sample heats 0.10 kg of water by 30°C. Calculate the energy gained by the water.
10. Explain why a simple food-calorimetry experiment usually underestimates the energy released by the food.
11. Give three ways a calorimetry experiment could be made more accurate.
12. A student obtains a specific heat capacity substantially different from the accepted value. Explain two experimental factors that could have caused the difference.