## Specific Heat Capacity The key formula in this topic is Q = mc𝛿θ.

Q: The heat energy gained (or lost) by a substance
m: The mass of the substance gaining (or losing) heat energy
c: Specific heat capacity
𝛿θ: The increase (or decrease) in temperature of the substance that is gaining (or losing) heat energy

Very often, the formula Q = mcθ is used instead. However, I strongly discourage the use of this variation until you are confident with the topic and understand what you are doing. This variation is not as accurate as Q = mc𝛿θ. Delta (𝛿) is the symbol that indicates change. When using this formula, we indeed substitute the value of the change in temperature (𝛿θ) – increase or decrease in temperature. No fixed temperature value is substituted in the formula.

We will start with exploring specific heat capacity before heat capacity because this is the variable most often used together with the key formula Q = mc𝛿θ.

Rearranging the formula and making specific heat capacity (c) the subject of the equation, we get: From the formula for specific heat capacity, we can see that specific heat capacity equals heat energy (Q) per unit mass (m) per unit change in temperature (𝛿θ). This is exactly what it is!

Specific heat capacity is the heat energy needed to raise the temperature of 1 kg of a substance (per unit mass) by 1 °C (per unit change in temperature).

The change in temperature is sometimes state as 1 K.
(See below for the full explanation) There are two units commonly used for specific heat capacity – J kg-1 °C-1 and J kg-1 K-1.

Two units for temperature are used here – degree Celcius (°C) and Kelvin (K).
Both are different temperature scales and have different values for specific temperatures. For example, the melting point of ice is 0 °C or 273 K.

However, the values for change in temperature are the same. For example, the change in temperature from 0 – 5 °C (273 – 278 K) is both 5 °C and 5 K.
They have the same value and therefore, both units can be used. ## Heat Capacity

From the formula for heat capacity, we can see that heat capacity equals heat energy (Q) per unit change in temperature (𝛿θ).

The only difference with specific heat capacity (see above) is that the value of this heat energy is NOT only to increase the temperature of 1kg of a substance but all of the substance.

Heat capacity is the heat energy needed to raise the temperature of a substance by 1 °C (per unit change in temperature).

For example, the specific heat capacity of a mug is the heat energy needed to raise the temperature of 1 kg of the mug by 1 °C.

Whereas, the heat capacity of a mug is the heat energy needed to raise the temperature of the whole mug by 1 °C. The two units commonly used for heat capacity are J °C-1 and J K-1.

(See above for the reason both can be used)

## Practical Application of Heat Capacity What is the use of heat capacity? How can we apply this piece of information?

Let’s say we supply 100J of energy to a substance with high heat capacity and the same amount of energy was supplied to another substance with low heat capacity.

What happens to the two substances? First, we need to understand the relationship between heat capacity and change in temperature.

Starting with the formula for heat capacity, we can deduce the following:

• Heat capacity is inversely proportional to the change in temperature.
• When a substance has a high heat capacity, it will experience a small change in temperature when supplied with heat energy.
• When a substance has a low heat capacity, it will experience a large change in temperature when supplied with heat energy.

This means that after both substances receive 100J of energy:

• The substance with a low heat capacity (blue) will have a higher temperature than the substance with a high heat capacity (red).
• The blue substance will have a higher temperature gradient with the surrounding than the red.
• Due to this, the blue substance will lose heat to the surrounding much faster than the red.

We can say that the red substance has a higher capacity to retain heat than the blue substance. ## Sea Breeze During the day:

• Both the land and sea receive the same amount of heat energy.
• The sea has a higher heat capacity than the land.
• The land has a greater increase in temperature than the sea.
• The layer of air above the land is heated up by a transfer of heat from the ground.
• Hot air expands and rises due to its lower density compared to the layer of colder air above it.
• The air above the sea is drawn in to fill the void left – this forms the sea breeze.

## Land Breeze During the night:

• Both the land and sea lose the heat energy.
• The sea has a higher heat capacity than the land.
• The land has a greater decrease in temperature than the sea.
• The layer of air above the sea is heated up by a transfer of heat from the sea.
• Hot air expands and rises due to its lower density compared to the layer of colder air above it.
• The air above the land is drawn in to fill the void left – this forms the land breeze.

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