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I came across a theory that proposed that earth's atmosphere must have had a density of 660 kg/m^3 during the mesozoic, and the gigantic size the dinosaurs attained on land was only possible due to the buoyant force such an atmosphere would provide.

This is obviously preposterous, but it got me wondering what would be the properties in a hypothetical atmosphere of such thickness, for example atmospheric pressure at sea level?

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    $\begingroup$ please post a link to your sources and show that you have tried to find an answer to your question. $\endgroup$ Commented Apr 23 at 3:21
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    $\begingroup$ You want a source for the theory? Its not really relevant but here you go dinosaurtheory.com/solution.html $\endgroup$
    – A.J
    Commented Apr 23 at 9:10

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If it were still behaving like an ideal gas, air at constant temperature would need to be under 660 times higher pressure in order for the density to be 660 times higher, so the pressure at sea level would have to be around 660 atm, or about 66 MPa.

However, approximating air as nitrogen, that pressure is far past the critical pressure of about 34 atm and normal Earth temperatures are well above the critical temperature as well (126 K), so an atmosphere of that density would have to be a supercritical fluid.

The short answer is that at 660 kg/m3 (and room temperature), you have a nitrogen-oxygen supercritical fluid ocean-like situation, not an atmosphere. The atmospheric pressure, wherever it became atmosphere, would be no more than 34 atm, but the air there would be much less dense than 660 kg/m3.

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