# How much will the atmospheric carbon dioxide change?

• unscientific
In summary: The correct so-called scale height of the atmosphere is close to 7 km, rather than 3 km. But an easier way of doing this problem is to determine the weight of a column of air above each square meter. That would be 105 N. Assuming that the gravitational acceleration does not change much over the first few km, the mass of air over each square meter of surface would be 104 kg. Multiplying this by the area of the earth, one obtains 1.3 x 1018 kg. This compares with a value of 1.2 x 1018 obtained by taking your answer and multiplying it by 7/3.
unscientific

## Homework Statement

Suppose ##10^{14} kg## of carbon dioxide was released into the atmosphere and absorbed completely, what is the percentage change of carbon dioxide concentration? Take initial atmospheric mass mixing ratio to be ## 5.7 \times 10^{-4} kg/kg##.

## The Attempt at a Solution

Using density of air as around ##29 g/mol##, the weight of the atmosphere is about ##10^{18} kg##. The percentage change is ##\frac{10^{14}}{10^{18}} \times 100 = 0.01%##? Where does the mixing ratio come in?

Please show us how you calculated the mass of the atmosphere.

Chet

Chestermiller said:
Please show us how you calculated the mass of the atmosphere.

Chet

Taking pressure to be ##p_0 = 10^5 Pa##, I used ##\frac{4}{3}\pi R_E^3 p_0 \sim 10^{18} kg##. Sorry the ##29g/mol## bit was misleading.

Last edited:
unscientific said:
Taking pressure to be ##p_0 = 10^5 Pa##, I used ##\frac{4}{3}\pi R_E^3 p_0 \sim 10^{18} kg##. Sorry the ##29g/mol## bit was misleading.
And (4/3) π RE3 represents what geometrically? Think about this carefully.

unscientific said:
Taking pressure to be ##p_0 = 10^5 Pa##, I used ##\frac{4}{3}\pi R_E^3 p_0 \sim 10^{18} kg##. Sorry the ##29g/mol## bit was misleading.
You can't just multiply the volume of the entire Earth by the air pressure at the surface of the Earth and think that you are getting the mass of the atmosphere. The units don't even match, and the Earth is not filled with air. What is the air density at the surface of the earth? Are you familiar with the barotropic equation?

Chet

Chestermiller said:
You can't just multiply the volume of the entire Earth by the air pressure at the surface of the Earth and think that you are getting the mass of the atmosphere. The units don't even match, and the Earth is not filled with air. What is the air density at the surface of the earth? Are you familiar with the barotropic equation?

Chet
Sorry I meant ##4\pi R_E^2 P_0##.

unscientific said:
Sorry I meant ##4\pi R_E^2 P_0##.
You forgot to divide by g.

Chet

The value ##29 (g/mol)## is equivalent to ## 1.29 (kg/m^3) ##. Taking the same density for about 3km and the Earth surface we have:
## \pi\times(6.4\times10^6)^2\times3000\times1.3 \approx 5\times10^{17} (kg) ##

For better answer we must use exponential law for pressure.

unscientific
theodoros.mihos said:
The value ##29 (g/mol)## is equivalent to ## 1.29 (kg/m^3) ##. Taking the same density for about 3km and the Earth surface we have:
## \pi\times(6.4\times10^6)^2\times3000\times1.3 \approx 5\times10^{17} (kg) ##

For better answer we must use exponential law for pressure.
The correct so-called scale height of the atmosphere is close to 7 km, rather than 3 km. But an easier way of doing this problem is to determine the weight of a column of air above each square meter. That would be 105 N. Assuming that the gravitational acceleration does not change much over the first few km, the mass of air over each square meter of surface would be 104 kg. Multiplying this by the area of the earth, one obtains 1.3 x 1018 kg. This compares with a value of 1.2 x 1018 obtained by taking your answer and multiplying it by 7/3.

Chet

unscientific

## 1. How does the amount of atmospheric carbon dioxide change over time?

The amount of atmospheric carbon dioxide changes over time due to natural processes such as photosynthesis and respiration by plants and animals, as well as human activities such as burning fossil fuels.

## 2. What are the main factors that affect atmospheric carbon dioxide levels?

The main factors that affect atmospheric carbon dioxide levels include the burning of fossil fuels, deforestation, and changes in land use. These activities release large amounts of carbon dioxide into the atmosphere, contributing to the overall increase in atmospheric carbon dioxide levels.

## 3. How much will the atmospheric carbon dioxide change in the future?

This is a difficult question to answer definitively, as it depends on a variety of factors such as future emissions, technological advancements, and natural processes. However, most scientific studies project that atmospheric carbon dioxide levels will continue to increase in the future.

## 4. What are the potential consequences of increasing atmospheric carbon dioxide levels?

The increase in atmospheric carbon dioxide levels can have a variety of consequences, including global warming, ocean acidification, and changes in weather patterns. These can have significant impacts on ecosystems, agriculture, and human health.

## 5. What can be done to reduce atmospheric carbon dioxide levels?

To reduce atmospheric carbon dioxide levels, we can take actions such as reducing our dependence on fossil fuels, promoting renewable energy sources, and implementing sustainable land use practices. Additionally, technologies such as carbon capture and storage can also help to remove carbon dioxide from the atmosphere.

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