Density, Pressure, and Temperature
For all of the entries in the table below (with the exception of Neptune's temperature) I have read the corresponding values off of figures in from the references. Given the modeling uncertainties I don't think there's much value in going beyond 1 or 2 significant figures.
For Neptune's temperature I used equation 5 from Interior models of Uranus and Neptune:
$$T = C\rho^\gamma$$
where $T$ is temperature, $\rho$ is density, and $C$ and $\gamma$ are model constants. Using the question specified density of 1 g/cm2 and the model defined value of $\gamma=0.5$ we can solve for $C$ given a known pressure / temperature pair and then compute the corresponding temperature at the desire pressure.
For Neptune, the paper assumes, for the 1-bar pressure level a density of $\rho = 4.38\times 10^{-4} g/cm^{-3}$ and a temperature $T=75K$. Substituting into the model and solving for $C$ (I'm ignoring units for now as they get goofy with this model):
$$75 = C\sqrt{4.38\times 10^{-4}}$$
$$C\approx3584$$
Now using this for a density of $\rho = 1 g/cm^{-3}$:
$$T=3584\sqrt{1}=3584$$
I will round this number to two significant figures in the table (3600 K).
Planet |
1 g/cm2 Depth (km) |
Pressure* (MBar) |
Temperature* (K) |
Jupiter |
15,500 |
2 |
6,500 |
Saturn |
23,900 |
2 |
5,000 |
Uranus |
6,100 |
0.5 |
4,800 |
Neptune |
4,700 |
0.4 |
3,600 |
*-At the 1 g/cm2 depth
Density Profiles
To address the question about the density in the lower atmosphere I am including plots from the references here.
Jupiter (Figure from Structures of the planets Jupiter and Saturn)

Saturn (Figure from Structures of the planets Jupiter and Saturn)

Uranus and Neptune (Figure from Interior models of Uranus and Neptune)

References
- Kerley, Gerald I. "Structures of the planets Jupiter and Saturn." arXiv preprint arXiv:1307.3094 (2013).
- Helled, Ravit, John D. Anderson, Morris Podolak, and Gerald Schubert. "Interior models of Uranus and Neptune." The Astrophysical Journal 726, no. 1 (2010): 15.
- Nettelmann, Nadine, K. Wang, Jonathan J. Fortney, Sebastien Hamel, S. Yellamilli, M. Bethkenhagen, and R. Redmer. "Uranus evolution models with simple thermal boundary layers." Icarus 275 (2016): 107-116.