Anything could happen from running Correctly for a certain time then the PC no longer boots, random BSOD, Crash/Freezes, Burning Components, PC wont turn on, Internal PSU faillure (smoke or blown fuse, i've seen both) and any thing that you can imagine... A good 500w like a Seasonic one (i have an Antec NeoHE 500w that have Seasonic internals) would easily run that (i had run 2X560ti + a Q6600 overclocked for years now) but this PSU was rated 500w continous output @50 clesius so it's 650-700w in reality so it really depend on the brand, the model and the price paid, a 80-100$ 500w is a lot more reliable than a 50$ 500w PSU...

What's the brand and the model of your PSU ???

If it's a cheap one, I'd strongly suggest that you invest on a better PSU (600w from a good brand like Antec, Corsair, Seasonic, Enermax, CoolerMaster are some suggestions) and buy a 7950 instead to not raise the budget too much as PSU is a costly components when you want a decent one... (i also recommend a 80+ Bronze at minimum and Gold or Platinum if possible with your budget...)

Best case scenario if the PSU wattage is insufficient is that the PSU will shut itself down to protect itself. Worst case scenario would be damage to other components and/or the PSU itself. Normally an overloaded PSU will cause a lot of system instability.

To answer your question about the 7970, a 500W PSU should be fine for that card. This follows the assumption that you are using a quality PSU and not simply a generic one.

500 watts will work for now. If you ever hit peak wattage, you will probably end up somewhere close to 400 watts. You should still consider a stronger Power Supply. In general, a PSU should run underneath 60% of its capacity. When it operates over this limit, it suffers in efficiency and the overall system is stressed to its limits which will decrease a PSU's lifespan as well as possible instability (this usually isn't a problem with quality PSUs). You should also check on your PSUs actual wattage verses its rated wattage.

I wouldn't worry about burning fires inside your computer, generally it would just shut off during random gaming events or not post at all.

A single Radeon HD 7970 graphics card from AMD specifies a minimum of a 500 Watt or greater power supply.

Generally these requirements are loosely based on a wide assumption that your power supply is somewhat good and that you only have the standard number of components installed. More specifically the 500watts requirement is about having enough Amps to power the video card and other devices.

The 7970 will claim about 25A (25-Amps) for itself. Check the specifications of your Power Supply to see if you can supply 25A. If your system meets those requirements and it doesn't lock up during heavy usage then you should be fine, but I'd recommended a PSU upgrade in the future.

Yeah I got the cheap one, CHIEFTEC 500W 80+ bronze. From what I read I see better not to risk. Thank you all.

It isn't necessarily bad. If Delta made that particular Chieftec PSU, then it is probably top notch.

Nah it's just cheap one I paid ~130LT/2.4= ~54 USD. And what about 7950 would 500W be enough? I have AMD Phenom II 1055T not overclocked for more info. And card that I think of buying is club 3d royalking, so it's overclocked and still has headroom for more.
And this is what it says at shop where I bought the PSU:
PS2 Form factor / 500 Watts Intel P4 / AMD Athlon XP / ATX 12V 2.3 Specification / 230V input / 120mm fan / active PFC (Power Factor Correction) / AFC (Automatic Fanspeed Control) / OVP (Over Voltage Protection) / SCP (Short Circuit Protection) / OCP (Over Current Protection) / MTBF: >100.000 h / 80% Efficiency only 230V

Personally, I think you'll be fine.

I'll give it a try then, thank you.

Yeah, just give it a try first. I did a search and could find a wide range of specs for that PSU and they mostly hinted at two 12v rails with 20A, so that would combine for 40a. This also reads as two 12v rails (20amps x 12volts) = 240watts, Then multiply that PSU rail by two and you really have a total of 480watts.

I had Q9300 and GTX275OC, but only 550w Power supply, I knew it was lack of power because the fan of my CPU was increasing speed automatically to full speed, the components were overheating especially the graphic card. After a year it died. (working with high temperatures for long time). After that I bought 1000w power supply and all went back to normal.

Not to sound cruel to any one person but this is a very bad idea and i don't think he should try it! No name PSUs usually don't have overload protection, PFC, quality caps, true wattage ratting, or high efficiency, and more! If you push a crap power supply even close to its rated limits, you risk damage. Without the safeguards like overload protection, PFC, ect, you risk horrible things like power spikes discharging into all the components, Poorly filtered DC current, which would result in damage. That's just off the top of my head. Your computer is not worth risking over the replacement cost of the PSU. EVEN if it does work, its pushed to its limit 24/7 it will fail sooner then later.

Sorry, just being devils advocate!

-TRM

If it's not a good brand power supply it will not supply the power written on it..
Don't forget the efficiency of power supplies!
Look at Efficiency level certifications first

Buy a name brand, quality power supply with at least a 3 year warranty.