Question

Explain why the concentration of ${\mathrm{CO}}_2$ in air is expected to rise linearly with time if its rate of emission remains a constant.

Short answer

The concentration of ${\mathrm{CO}}_2$ rises linearly with time because a constant emission rate adds a fixed amount of ${\mathrm{CO}}_2$ to the atmosphere every year.

Step-by-step solution

Understand the Concept of Emission and Concentration

The rate of emission refers to the amount of ${\mathrm{CO}}_2$ added to the air per unit time. If this rate is constant, the same amount of ${\mathrm{CO}}_2$ is added to the atmosphere every year.

Recognize the Cumulative Effect

Every year, the cumulative concentration of ${\mathrm{CO}}_2$ increases by the same amount. For example, if the emission rate is 10 units per year, in year one the concentration increases by 10, in year two by another 10, and so on.

Define Linear Growth

Linear growth means that the addition to the total is constant over time. In this context, it means that the increase in ${\mathrm{CO}}_2$ concentration each year is the same as it was the previous year.

Link Emission Rate to Linear Increase in Concentration

Since the emission rate is constant, each year there is a predictable and steady increase in the concentration of ${\mathrm{CO}}_2$. This steady increase is represented as a line with a constant slope if you plotted concentration over time.

Conclusion

Therefore, if the rate of emission of ${\mathrm{CO}}_2$ stays constant, the concentration in the atmosphere increases in a linear pattern, meaning it increases by the same amount every year.

Key concepts

Constant Emission Rate

When we talk about a constant emission rate of carbon dioxide (${\mathrm{CO}}_2$), we mean that a fixed amount of ${\mathrm{CO}}_2$ is released into the atmosphere every year. Let's visualize this concept: imagine a tap steadily dripping water into a bucket.

• The drip rate stays the same.
• The amount of water collected increases with each drip.

In the same way, a constant emission rate indicates a continuous and unchanging addition of ${\mathrm{CO}}_2$ into the atmosphere over time.

Linear Growth

With a constant emission rate, we witness linear growth in ${\mathrm{CO}}_2$ concentration. Linear growth describes a consistent increase in quantity over uniform intervals of time.
Consider planting one tree every year; after five years, you will have five trees. It's a steady accumulation.
For ${\mathrm{CO}}_2$, it means if we look at a timeline, the concentration increases by the same amount each year.
This is represented as a straight line when graphed, with a slope that reflects the rate of emission.

Cumulative Concentration

Cumulative concentration refers to the total amount of ${\mathrm{CO}}_2$ amassed in the atmosphere. Each year's emissions stack upon the previous year's, building up over time.

• If we add 10 units each year, the total concentration after 5 years is 50 units.
• This build-up doesn't reset each year; it carries over, accumulating like savings in a bank account.

Thus, even with a constant emission, the cumulative concentration rises annually, setting the stage for continued linear growth.

Atmospheric Chemistry

Atmospheric chemistry studies the chemical composition and reactions occurring in Earth's atmosphere. This field helps us understand how different factors, like ${\mathrm{CO}}_2$ emissions, affect climate.

• Atmospheric chemistry explains how ${\mathrm{CO}}_2$ interacts with other substances and contributes to phenomena like the greenhouse effect.
• It also involves studying the balance between natural absorption processes and the surplus from human activity.

Learning about atmospheric chemistry allows us to predict changes in ${\mathrm{CO}}_2$ levels and their broader implications on global temperatures and weather patterns.