Heat Capacity

Heat Capacity

Some materials require more energy to be added or removed for the same temperature change as other materials. This property is call heat capacity.

Note that large objects (an ocean being warmed by climate change) can store lots of energy for a small change in temperature. Also note that for equal masses, some materials require less energy for a change in temperature. To understand this we use the terms intensive and extensive.

Intensive vs Extensive Properties

• Intensive or bulk property

  • Does not depend on the amount of material

  • Example: temperature, density

• Extensive property

  • Depends on the amount of material

  • Example: mass, volume

Heat Capacity

• When heat moves from one material to another one temperature rises the other falls

• The temperature rise occurs as heat increases the motion of atoms in the material

• The rate of change in temperature with added energy is dictated by the heat capacity

• Ratio of heat added to temperature change

Heat Capacity

• Extensive property (of the material and the amount)

• Measured in Joules per degree Kelvin

Specific Heat Capacity

• Intensive property (of the material only)

• Measured in Joules per mass per degree Kelvin

Table of Specific Heat Values

Material	Heat Capacity (Joule/gram/kelvin)
Air	1
Water	4.1813
Iron	0.45
Aluminum	0.897
Brick	0.840
Wood	1.2 - 2.9

Partial list from https://en.wikipedia.org/wiki/Heat_capacity

Heat capacity

We have an equation that tells us how the energy absorbed by a material is related to the temperature rise.

$Q = mc\Delta T$

• $Q$ is energy transferred to or from substance
• $m$ is the mass
• $c$ is the specific heat capacity
• $\Delta T$ is the temperature change

Units

In metric units

• energy is in joules

• mass is often in grams

• specific heat is often in joule/gram/Kelvin

• the temperature difference is in Kelvin or Celsius

In english units

• energy is in BTU

• mass is in lbs

• specific heat is in BTU/lb/Fahrenheit

• the temperature difference is in Fahrenheit

Energy required for tea

How much energy does it take to make a cup of tea? Assume the water starts at 20C and is raised to 95C for a delta T of 75C. Further assume that there is 200 ml of water (200 grams).

$Q = mc\Delta T$

$Q = 200 grams \cdot 4.18 Joule/gram/kelvin \cdot 75K$

$Q = 63 kJ$

Relation to Buildings

• Thermal mass is added to a building to store heat

• Cool or warm air is passed through a building to deliver or remove heat.

Relation to Weather and Climate

• The heat capacity of water affects the climate in some areas

Rate of increase

If we have a source of constant thermal power and assume that all that energy is going into an object, we can calculate the rate of temperature rise of that object.

$Q = mc\Delta T$

We divide both sides by time.

$\frac{Q}{t} = \frac{mc\Delta T}{t}$

Remember that Q is an energy. That means Q over t is a power.

$P = \frac{mc\Delta T}{t}$

If we rearrange this equation algebraically, we see that

$\frac{P}{mc} = \frac{\Delta T}{t}$

This means that the power divided by the heat capacity gives you an estimate of the rate of temperature increase in an object.