ramish :
will 7850 run on a corsair cx 430w (http://www.corsair.com/power-supply-units/builder-series/builder-series-cx430-v2-80plus-certified-power-supply.html) with core i5 as processor and 2 sticks of 4gb ddr3 ram.i'll be gaming alot.
With an adapter, if you really want to,
based on nothing more strenuous than gaming
watercooled, overclocked I7-965 / X58 system with 7850
256 watts from the wall running a "game like" application, ~90% efficient psu, ~ 230 watt DC load
http://www.guru3d.com/article/amd-radeon-hd-7850-and-7870-review/7
"On average we are using roughly 50W to 100 Watts more than a standard PC due to higher CPU clock settings, water-cooling, additional cold cathode lights etc."
An I7-965 / X58 combo draws a good deal more power than an I5-2500K / P67
http://www.silentpcreview.com/article1245-page3.html
Part of the difference in power consumption in the above article is attributed to the power difference of the 5870 v 6870, can see that in the charts here
http://www.techpowerup.com/reviews/HIS/Radeon_HD_6870/27.html
Now back to the chart in the guru3D review and see that they calculate the difference in power consumption between the 6870 and 7850 at 32 watts
Would it be optimal ? no
Would you have room to upgrade or overclock ? not much
Can it be done ? absolutely