The 1st law of thermodynamics that you are ignoring is not the Stefan-Boltzmann law.
You are also trying to change the equation for the Stefan-Boltzmann law, making it something other than what it is.
You cannot create energy out of nothing. You are still ignoring the 1st law of thermodynamics.
Spectroscopy does not measure temperature, Poorboy.
You cannot blame your problem on me or anybody else, Poorboy.
Let's explain this in simple terms.
Electromagnetic radiation is energy.
Heat transfer occurs with radiation.
Spectroscopy measures the wave lengths at which molecules absorb and radiate electromagnetic energy.
The first law of thermodynamics says that energy can not be created or destroyed but can be transferred.
The atmosphere allows some electromagnetic radiation to pass through it. If it didn't we would not have visible light.
By changing the composition of the atmosphere we know we can change the energy that is absorbed by that atmosphere when electromagnetic radiation passes through it. This is clear because of spectroscopy and also because of Stefan-Bolzmann law which says that different materials have different emissivity coefficients.
The warming of the atmosphere does not violate the first law of thermodynamics. Any claim that the gas can't warm and therefor warm the earth is the violation of the first law. By changing the atmosphere it simply changes the amount of radiation it absorbs which means there is not a violation of the first law.
By changing the atmosphere composition it changes the wavelengths of electromagnetic radiation that is absorbed. To claim it doesn't change the wavelengths absorbed is a violation of Stefan-Bolzmann law.
The result is that the warming of the earth doesn't violate either the first law of thermodynamics of Stefan-Boltzmann law. Any claim that they do violate them is not supported by science.
Global warming can happen because the earth is an open system that gets energy from the sun. To claim that gas can't warm denies the first law of thermodynamics since the earth is an open system with a continuous energy source providing energy to the earth.