Can in a sole vessel be demonstrated that the air temperature rises when CO2 concentrations rises by sun irridation?
Were there yet any trials to test the effect of increasing C02 concentrations in rates like of 300 ppm, 400 ppm, 500 ppm, 1000 ppm CO2 to prove that CO2 rises also air temperature in an simple experiment?
And how much air temperature rises, when there is the air only zero, 100 ppm and 200 ppm CO2?
One of the most remarkable aspects of the paleoclimate record is the strong correspondence between temperature and the concentration of carbon dioxide in the atmosphere observed during the glacial cycles of the past several hundred thousand years. When the carbon dioxide concentration goes up, the temperature goes up. When the carbon dioxide concentration goes down, the temperature goes down. A small part of the correspondence is due to the relationship between temperature and the solubility of carbon dioxide in the surface ocean, but the majority of the correspondence is consistent with feedback between carbon dioxide and climate. These changes are expected if Earth is in radiative balance, and they are consistent with the role of greenhouse gases in climate change. While it might seem simple to determine cause and effect between carbon dioxide and climate from which change occurs first, or from some other means, the determination of cause and effect remains exceedingly difficult. Furthermore, other changes are involved in the glacial climate, including altered vegetation, land surface characteristics, and ice-sheet extent.
https://www.ncdc.noaa.gov/sites/default/files/Temperature-change-and-carbon-dioxide-change-measured-from-the-EPICA-Dome-C-ice-core-in-Antarctica-v2.jpg
Regards
My understanding of the system, and your question, is that a "sole" vessel might not lead to really informative results.
I have assumed your sole vessel is a transparent chamber of some kind, and empty bar gasses.
I suspect the air temperature, CO2 concentration and solar irradiation, in the sole vessel you mention, might not provide a complete system.
Unless of course the sole vessel you mention is something like a planet, with an atmosphere and so on.
Just shine infra-red light on vessel and temp will rise faster the higher the CO2 conc. This is basically the mechanism for warming in the atmosphere and is so well understood that one way we measure atmospheric CO2 concs is using absorption of infra-red light