I've skimmed through most the replies and what I haven't seen anyone say (although I could have missed it) is that for high graphics video card, and PSU combinations, the most often overlooked but most crucial thing to look at is
REQUIRED/PROVIDED AMPERAGE. Let me explain, you can have 2 500 watt powers supplies side by side, one with crappy 18amps total continuous amperage and the other with good 24-30Amp continuous amperage. If the card, in this case the 7850, requires @22amps at full load (which it does see calculations below in point 2.) then the card will work fine at full load with 24-30Amp powers supply and random reboot at full load on the 18Amp powersupply when power draw goes up during gaming load.
AND THEY ARE BOTH 500w POWERSUPPLIES SO YOU CAN'T GO ON WATTAGE ALONE. Likewise, you can buy a nice Seasonic x650 with Gold efficency and "Crossfire certified" BUT with only 54amps on a single 12v and that's NOT going to run 2 OC'd 7850s in Xfire because as calculated below you're gonna want AT LEAST 60amps total. Thus, the only thing you'll Xfire is 2 weaker cards like 7770s OR 2 low power (single fan small cards) 7850s at STOCK clocks. Most people you ask about OCing a video card as it relates to power draw will talk in "watts" but what they are missing (or not clarifing) is that watts relate to AMPS and the AMPS is what you really want from your PSU for nice gaming video cards and OCing. Read below (2).
IMPORTANT THINGS TO KNOW:
1. You want a single 12V rail if your going for gaming and gaming video cards, they are more efficent and no power loss/drop off the rail. For more on that go to hardwaresecrets.com and read their tutorial on "The Anatomy of Switching Powersupplies"
http://www.hardwaresecrets.com/article/327 it's excellent! The dual 12v Rails are more for servers IMO because if one rail fails the psu will still limp along over night till it's replaced in the morning. If it's in a game rig, and you loose a rail, you're probably gonna reboot anyways because it won't be able to handle the amperage with only one rail working in a dual rail powersupply thus it will just reboot and you'll be replacing it and it won't really limp you through the night anyways.
2. Depending on the review/and card you pick, the average Radeon 7850 TPD (total power draw) seems to draw between 222Watts and 274 Watts at full load for the more efficent cards like the powercolor, diamond and VisionTek. These are all single fan models. We're not concerned with idle power draw in this calculation cause you're not going to play BF3, Skyrim, SWTOR, D III or anything else at idle lol! Now here's the important part based on that info. Watts divided by Volts = amps. In mathimatical form, W/V=Amps. So, 222W/12v = 18.5 amps and 274W/12v = 22 amps. That's your average required amperage for the above mentioned styles 7850. Now this does not take into account leakage, efficency etc etc.. but it is a good general basis that says on REFERENCE CLOCKS (what the card comes set at) at full load you'll need at least 22amps... And, since digging around on the net can produce AMD material that states the older 6850 required 24amps minium, 22 amps for the newer less power hunger 7850s sounds legit...
Also, that's at REFERRENCE clocks .. if you over clock you're gonna want some head room so I would suggest a MINIMUM of 30amps on a single 12V rail as a good starting point for a powersupply. You can find 30amp 12V 550 watts all over newegg and I've got one from UlTRA a 550W LSP myself (although efficency drops after a year).
SO, to answer your question, YES it will work on a 500W powersupply PROVIDED it has atleast 22Amps minimum; but, at miniumum expect it to reboot if it's older or less efficent, especially if you pack in a bunch of Hard-drives because sata drives can also share the 12v rail. To be safe I'd check to make sure you have AT LEAST a nice 30amp single 12v PSU, especially if you want to OC, if not buy a new one... Might I suggest this one >
http://www.newegg.com/Product/Product.aspx?Item=N82E16817207013 It's 44amps but cheaper than the 500watt ones with the criteria of single 12 rail and active PFC. You can check your current powersupply either by manufacturer's webpage, the box or the label on the PSU it self. Look for the +12V box on the grid... I should say "30A" miniumum to be safe because the hard-drives ALSO share power with the 12v rail; and, to allow headroom for ocing and decline in efficency over it's life span.
Personally, if you're going to OC + OV and Xfire, I'd go with a 70Amp 850W MINIUM powersupply like the XXX PRO 850 from XFX that's built similar in design to Seasonic and by the same parent manufacturer that builds both; but, the XFX XXX PRO 850 is about $40-$50.00 cheaper. Also, at 70amps that gives you 5amps per card headroom over OC minimum of 30amps per card AND that's CONTINUOUS RATING.. the max amperage will probably be around 86Amps but that's not sustainable. For an echo effect > if you plan to OC+OV and XFire get at least a 850W gold/silver PSU with proper connections and be done with it.
http://www.newegg.com/Product/Produc...82E16817207017
REMEMBER > AMPERAGE IS KEY! Ignore the post for wattage draw "from the wall" lol because (you'll most likely under amp the card and it will run fine at idle then reboot at load) they are going by what the PSU draws and that's not what you want...You want WHAT THE VIDEO CARD DRAWS and the key to that is AMPERAGE. "Wattage from the wall " calculations is what you get when you let an electrician pick your powersupply and not a PC hardware specialist or tech lol. Again, You can have one 500Watt psu at 18amps and one 500W psu at 24-30amps and the one with higher amps (provided it meets the minium required by the video card to run at load) will run your card at full load the 18amp one WILL reboot just when you're getting your frag on ... lol. For OCing add about 8-10amps headroom. Trust me I used to sell new powersupplies with high end video cards all day long because customers didn't know the difference between wattage and amperage and what to look at most in a PSU for higher end gaming cards... the answer = amperage. I pick ALL my PSUs for gaming rigs based on AMPERAGE, Single 12v Rail, Electric Signal Noise, Max load and Efficency and the most important factors to me above all is 1. Single 12V Rail 2. Amperage. The rest is icing.
Welcome to the wonderful (and expensive) world of properly suppling power to a good video card and over clocking. Good luck