## 50 Years to Net-Zero

A country wishes to achieve net-zero CO2 emissions in 50 years.

At the start of the program their emissions are 800MtCO2 year-1.

They decide that they will be able to reduce their emissions at a stable rate so that each subsequent year they emit 12MtCO2 less than the previous year.

a) Calculate the total emissions that the country had produced over the 50 years, giving your answer in MtCO2.

[2 marks]

b) Show that a graph of MtCO2 produced per year against the year follows a straight line with equation:

$y = 800 – 12x$

[1 mark]

At the same time as reducing their emissions, the country decides to start a carbon dioxide removal program, whereby a certain amount of carbon dioxide is captured from the atmosphere and sequestered underground each year.

The program begins in the tenth year.

When the graph of MtCO2 removed per year is plotted against the year, it follows the curve with equation

$y = 0.1x^{2} – x$

c) Determine whether the country achieves their goal by finding the year in which the emissions removed are equal to the emissions produced, and thus the net emissions from the country are zero.

[3 marks]

After the 50 year program, the countries emissions stabilise at the final value.

The MtCO2 absorbed per year follows the same trend as before.

The country wishes to have not contributed to global warming at all since the start of the program. To achieve this, their net total CO2 emissions over the entire program would have to be zero.

d) Given the above information, by using calculus show that it takes 109 years for the country to have had a net zero effect on global warming since the start of the study.

[5 marks]

## Storing Sequestrates

A manufacturer produces a tank for storing liquid CO2 underground.

The tank is modelled in the shape of a hollow vertical circular cylinder closed with a flat lid at the top and a hemispherical shell at the bottom.

The walls of the tank are assumed to have negligible thickness.

The cylinder has a radius r metres and height h metres and the hemisphere has radius r metres.

The volume of the tank is 6 m3.

a) Show that, according to the model, the surface area of the tank, in m2 is given by

$\frac{12}{r} + \frac{5}{3}\pi r^{2}$

[4 marks]

The manufacturer needs to minimise the surface area of the tank, to minimise costs.

b) Find, using calculus, the radius of the tank for which the surface area is a minimum.

[4 marks]

c) Find the surface area of the tank for this radius, giving your answer to the nearest integer.

[2 marks]

## CCS Container

Carbon capture and storage is method of removing carbon dioxide from the atmosphere and storing it as a liquid underground. Carbon capture and storage is one possible method of slowing climate change.

Throughout this question you may ignore the mass of the container and consider only the mass of the liquid carbon dioxide that it contains. The liquid carbon dioxide is stored in a cylindrical container of volume 3.8m3.

a) The density of liquid carbon dioxide is 1100kg/m3.

Work out the mass of the liquid carbon dioxide.

[2 marks]

The 3.8m3 cylinder container of liquid carbon dioxide has a base of radius 0.5m.

b) Work out the height of the cylinder. Give your answer to 3 significant figures.

[2 marks]

## A New Power Station

A new kind of gas-fired power station releases on average 1.73×104 kg of pure carbon dioxide (CO2) every day. It also uses the heat of exhaust gases to provide community heating so the carbon dioxide leaving the power station is at same temperature as the environment. The density of CO2 as it leaves the power station is 1.98 kg/m³.

a) What volume of pure CO2 will be emitted from the power station each day?

[2 marks]

The CO2 now enters the atmosphere and is ‘diluted’ by other air molecules and therefore occupies a larger volume. In the atmosphere, for every million (1000000) air molecules, there are 400 CO₂ molecules.

b) Work out the volume that the diluted CO2 will now take up in the atmosphere. Give your answer to 3sf.

[2 marks]

A new technology is added to the power station to capture this carbon dioxide and store it as a liquid.

c) The density of liquid carbon dioxide is 1100kg/m³.

Work out the volume that the amount carbon dioxide produced every day will occupy if stored as a liquid.

[2 marks]

A depleted oil field contains a reservoir of area 1150 m2 which is 150m deep. This reservoir could be used to store the liquid carbon dioxide.

d) Evaluate how many years’ worth of carbon dioxide emitted from the power station could be stored in this oil field. Give your answer to two significant figures.

[3 marks]

## Rainforest Reforestation

One way of reducing carbon dioxide in the atmosphere and slowing global warming is to plant trees which absorb carbon dioxide from the atmosphere.

A scientist plants some trees in the Amazon rainforest and the Tongass rainforest.

The scientist compares the carbon dioxide absorbed from the atmosphere by the trees she planted in the Amazon rainforest with the trees she planted in the Tongass rainforest.

Amazon

 Carbon absorbed per tree $$\frac{1}{5}$$ more than in the Tongass Number of trees planted $$\frac{1}{4}$$ less than in the Tongass

By what fraction is the total carbon dioxide absorbed by the trees planted in the Amazon compared with the total carbon dioxide absorbed by the trees planted in the Tongass rainforest?
[3 marks]