CFC-11 and CFC-12 are very potent greenhouse gases. Suppose the emission of 1 Tg of CFC-11 causes a 1.0 W m-2 instantaneous perturbation in the radiation budget. The emission of the 1 Tg of CFC-12 causes a 1.5 W m-2 radiative forcing.

The 100 year global warming potential for CFC-11 is estimated to be 4750. Global warming potential is a measure of how much energy would be trapped by the emission of one molecule of a given gas over a specified time period, in this case 100 years, relative to CO2. Global warming potential depends on both the atmospheric lifetime of a gas, as well as its ability to absorb infra-red radiation.

Use the information on the lifetimes and relative radiative forcing strengths of CFC-11 and CFC-12, as well as the global warming potential of CFC-11 to estimate the global warming potential of CFC-12. You may assume that the radiative forcing of each species is simply proportional to its concentration.

Hint: Use the model from part (a) to calculate the total energy absorbed by the instantaneous injection of 1 Tg of each CFC into the atmosphere over 100 years. The ratio of these two energies is the ratio of the global warming potentials.

Model from Part (a) is

dC/dt = E - (C/tau)
C - concentration of the gas [Tg]
E - emission rate [Tg/yr]
t - time [yr]
tau - represents the lifetime of the gas in the atmosphere, before it is removed, either by chemical reactions or deposition to the surface [yr]

To calculate the global warming potential (GWP) of CFC-12 using the information given, we can use the ratio of the energies absorbed by the injection of 1 Tg of CFC-11 and 1 Tg of CFC-12 over 100 years.

Let's start by calculating the energy absorbed by the injection of 1 Tg of CFC-11 over 100 years:
Energy absorbed by CFC-11 = (1 Tg) * (1.0 W m^-2) * (100 years)

Next, let's calculate the energy absorbed by the injection of 1 Tg of CFC-12 over 100 years:
Energy absorbed by CFC-12 = (1 Tg) * (1.5 W m^-2) * (100 years)

Now, calculate the ratio of the energy absorbed by CFC-12 to that absorbed by CFC-11:
GWP of CFC-12 / GWP of CFC-11 = (Energy absorbed by CFC-12) / (Energy absorbed by CFC-11)

Finally, use the known GWP of CFC-11 to calculate the GWP of CFC-12:
GWP of CFC-12 = (GWP of CFC-11) * (GWP ratio)

Since the GWP of CFC-11 is given to be 4750, substitute this value into the equation:
GWP of CFC-12 = 4750 * (GWP ratio)

The GWP ratio is obtained from the previous calculation: the ratio of the energy absorbed by CFC-12 to that absorbed by CFC-11.

By following these steps, you can estimate the global warming potential of CFC-12 using the provided information.