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D3.3 · Relate heat transfer to mass, heat capacity, and temperature change

Learn to relate heat transfer to mass, heat capacity, and temperature change through clear examples and targeted practice.

Ontario Grade 12 Chemistry

Energy Changes and Rates of Reaction

Ontario Grade 12 Chemistry — study topic D3.3

A small cup of water and a large pot of water can both be warmed, but the larger amount usually needs more energy to reach the same temperature increase. This observation connects three quantities: how much material is present, how readily that material changes temperature, and how much its temperature changes. In this lesson, heat transfer means energy moving from one object to another because they have different temperatures. The lesson uses that meaning to relate heat transfer to mass, heat capacity, and temperature change.

What you will learn

  • Describe heat as energy transferred between objects at different temperatures.
  • Explain how mass and heat capacity affect the temperature change caused by heat transfer.
  • Use the relationship between heat transfer, mass, specific heat capacity, and temperature change.
  • Choose an appropriate sign and report a calculated heat transfer with units and significant digits.

1. From an observation to a particle model

Temperature describes how hot or cold something is. A temperature change is the final temperature minus the initial temperature. For example, warming water from 20.0 ∘C20.0\ ^\circ\mathrm{C} to 30.0 ∘C30.0\ ^\circ\mathrm{C} gives a temperature increase of 10.0 ∘C10.0\ ^\circ\mathrm{C}. A temperature change can also be negative when an object cools.
Heat is energy transferred because of a temperature difference. When a warm object touches a cooler one, energy transfers from the warmer object to the cooler one. The warmer object loses energy as the cooler one gains energy. Heat is not the same thing as temperature: heat is transferred energy, while temperature tells us how hot or cold an object is.
At the particle level, particles in warmer matter have greater average motion than particles in cooler matter. When the objects interact, energy transfers through their particles. This model helps explain why a temperature can change when energy enters or leaves an object. It does not mean that temperature itself is transferred.
Mass is the amount of matter in a sample. If two samples of the same material undergo the same temperature increase, the sample with more mass generally requires more transferred energy. It contains more material whose temperature is changing.
ΔT=Tfinal−Tinitial\Delta T=T_{\mathrm{final}}-T_{\mathrm{initial}}
  • Heat is energy transferred because of a temperature difference.
  • Mass measures the amount of matter in a sample.
  • A temperature change is final temperature minus initial temperature.

2. Heat capacity and specific heat capacity

Heat capacity describes how much energy must be transferred to change the temperature of an entire object by one degree Celsius. Its symbol is CC, and its common unit is joules per degree Celsius, written J/∘C\mathrm{J}/^\circ\mathrm{C}. A larger heat capacity means that more energy is needed for the same temperature change.
Specific heat capacity describes how much energy is needed to change the temperature of one gram of a material by one degree Celsius. Its symbol is cc. Its common unit is J/(g ∘C)\mathrm{J}/(\mathrm{g}\, ^\circ\mathrm{C}). Specific heat capacity is a property of the material; heat capacity applies to the whole sample or object.
For the same material, a larger sample has a larger heat capacity because it contains more mass. In this lesson, the specific heat capacity is treated as constant over the temperature change being considered. Water is often used as a reference material in course calculations; its specific heat capacity is approximately 4.18 J/(g ∘C)4.18\ \mathrm{J}/(\mathrm{g}\, ^\circ\mathrm{C}).
The relationship shows that the heat transferred to or from a sample depends on its mass, its specific heat capacity, and its temperature change. If the mass or specific heat capacity is larger, the same heat transfer produces a smaller temperature change. If the temperature change is larger, more heat has been transferred for the same sample and material.
q=mcΔTq=mc\Delta T
  • Heat capacity, CC, applies to a whole object.
  • Specific heat capacity, cc, applies per unit mass of a material.
  • A greater mass or specific heat capacity means more energy is needed for the same temperature change.

3. Using the relationship and signs

In the equation, qq is the heat transferred to or from the sample, measured in joules. The symbol mm is the sample mass, and cc is its specific heat capacity. The symbol ΔT\Delta T is the temperature change. The product of mass and specific heat capacity is the heat capacity of that sample, so the same relationship can also be written using CC.
Use a consistent sign convention. If the sample warms, its final temperature is higher than its initial temperature, so ΔT\Delta T and qq are positive. The sample has gained heat. If the sample cools, both are negative. The sample has lost heat. This sign describes heat transfer for the sample being studied.
The units provide a useful check. Multiplying grams by joules per gram per degree Celsius and then by degrees Celsius leaves joules. The units of temperature change can be written in degrees Celsius for this calculation; the size of a one-degree Celsius change is the same as a one-kelvin change.
Before calculating, identify the sample, record its initial and final temperatures, and find its temperature change in that order. Then select the specific heat capacity for the material, substitute values with units, and check whether the sign agrees with warming or cooling. Round the final value to match the precision of the given measurements.
C=mcC=mc
  • Use ΔT=Tfinal−Tinitial\Delta T=T_{\mathrm{final}}-T_{\mathrm{initial}}.
  • For the sample, warming gives positive qq; cooling gives negative qq.
  • Check that the calculated unit is joules.

4. Reading the relationship qualitatively

The equation can be used to predict how changing one quantity affects another. For a fixed material and a fixed mass, transferring more heat produces a greater temperature change. For the same amount of heat transferred to equal masses, the material with the larger specific heat capacity has the smaller temperature change.
Mass also matters when comparing samples. For equal materials receiving equal amounts of heat, the sample with the greater mass changes temperature less. These comparisons assume the stated quantities are the only ones changing. They help explain why a small amount of a material may warm noticeably while a larger amount of the same material warms less under the same heat transfer.
Do not use the equation to treat heat and temperature as interchangeable. A sample can receive heat without having a large temperature change if its mass or specific heat capacity is large. The equation connects the quantities; it does not say that the numerical value of heat is a temperature.
When answering a question, distinguish between a numerical calculation and a comparison. A calculation needs values and units. A comparison can use the direction of the relationship: at fixed mass and material, more heat means a larger temperature change; at fixed heat and material, more mass means a smaller temperature change.
  • At fixed mass and material, greater heat transfer gives a greater temperature change.
  • At fixed heat transfer and material, greater mass gives a smaller temperature change.
  • At fixed heat transfer and mass, greater specific heat capacity gives a smaller temperature change.

Worked example

Finding the heat gained by water

A 250 g250\ \mathrm{g} water sample warms from 20.0 ∘C20.0\ ^\circ\mathrm{C} to 31.6 ∘C31.6\ ^\circ\mathrm{C}. Use c=4.18 J/(g ∘C)c=4.18\ \mathrm{J}/(\mathrm{g}\, ^\circ\mathrm{C}). Calculate the heat transferred to the water.
  1. Find the temperature change
    Subtract the initial temperature from the final temperature. The positive result is consistent with the sample warming.
    ΔT=31.6 ∘C−20.0 ∘C=11.6 ∘C\Delta T=31.6\ ^\circ\mathrm{C}-20.0\ ^\circ\mathrm{C}=11.6\ ^\circ\mathrm{C}
  2. Substitute with units
    Use the mass of the water and its specific heat capacity. The units cancel to give joules. Since 250 g250\ \mathrm{g} has two significant figures as written, the final result must be rounded to two significant figures.
    q=(250 g)(4.18 J/(g ∘C))(11.6 ∘C)=1.2×104 Jq=(250\ \mathrm{g})(4.18\ \mathrm{J}/(\mathrm{g}\, ^\circ\mathrm{C}))(11.6\ ^\circ\mathrm{C})=1.2\times10^4\ \mathrm{J}
  3. Interpret the result
    The calculated heat is positive, so the water gained energy. The rounded value has two significant figures, matching the least precise given measurement.
    q=+1.2×104 Jq=+1.2\times10^4\ \mathrm{J}
Answer: The water gains 1.2×104 J1.2\times10^4\ \mathrm{J} of heat.
Check: The temperature rose, so the heat transfer for the water should be positive. The result has units of joules and is rounded to two significant figures.

Common mistakes and how to avoid them

Using the initial temperature minus the final temperature for every problem.
Correction: Find temperature change as final temperature minus initial temperature. Cooling then naturally gives a negative change.
Calling specific heat capacity the heat capacity of the whole sample.
Correction: Specific heat capacity is per unit mass. The sample's heat capacity is the specific heat capacity multiplied by its mass.
Assuming a higher temperature always means more heat was transferred.
Correction: Heat transfer depends on mass, specific heat capacity, and temperature change together. Temperature alone does not give the heat transferred.
Reporting a heat transfer without units or with a sign that conflicts with warming or cooling.
Correction: Use joules for heat transfer and check the sign against the sample's temperature change.

Lesson summary

  • Heat is energy transferred because of a temperature difference.
  • Specific heat capacity describes the energy needed per gram per degree of temperature change.
  • The heat transferred to or from a sample is related to its mass, specific heat capacity, and temperature change.
  • For a sample, warming corresponds to positive heat transfer; cooling corresponds to negative heat transfer.

Check your understanding

Question 1

Two equal-mass samples receive the same amount of heat. Sample A has a greater specific heat capacity than Sample B. Which sample has the smaller temperature change?
  1. Sample A
  2. Sample B
  3. They must have equal temperature changes
  4. There is not enough information to compare them
Show answer and explanation
Sample A
For equal heat transfer and mass, the sample with the greater specific heat capacity has the smaller temperature change.

Question 2

A sample cools from 48.0 ∘C48.0\ ^\circ\mathrm{C} to 39.0 ∘C39.0\ ^\circ\mathrm{C}. What is its temperature change?
  1. +9.0 ∘C+9.0\ ^\circ\mathrm{C}
  2. −9.0 ∘C-9.0\ ^\circ\mathrm{C}
  3. +87.0 ∘C+87.0\ ^\circ\mathrm{C}
  4. −87.0 ∘C-87.0\ ^\circ\mathrm{C}
Show answer and explanation
−9.0 ∘C-9.0\ ^\circ\mathrm{C}
Final minus initial gives 39.0 ∘C−48.0 ∘C=−9.0 ∘C39.0\ ^\circ\mathrm{C}-48.0\ ^\circ\mathrm{C}=-9.0\ ^\circ\mathrm{C}, which is negative because the sample cooled.

Question 3

For the same material and the same heat transfer, what happens to the temperature change if the sample mass increases?
  1. It increases.
  2. It decreases.
  3. It stays the same.
  4. It becomes negative in every case.
Show answer and explanation
It decreases.
A larger mass has a larger heat capacity for the same material, so the same heat transfer produces a smaller temperature change.

Key terms

Heat transfer
Energy moving from one object to another because they have different temperatures.
Mass
The amount of matter in a sample.
Temperature change
The final temperature minus the initial temperature.
Heat capacity
The energy needed to change the temperature of a whole object by one degree.
Specific heat capacity
The energy needed to change the temperature of one gram of a material by one degree.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 12 Chemistry (SCH4U), expectation D3.3. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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