will AMD Radeon HD 7970 works on Pentium(R) Dual-Core CPU 2.50ghz ?

Technically speaking any VGA will work with any processor, provided that the board has support for the card (PCI E 1.0, 1.1 , 2.0 etc(all backward compatible) or AGP).
So if you have a PCI E slot ur good to go however there will be a major bottleneck.
 
Graphics card compatibility is motherboard dependent and not cpu dependent. If your motherboard have PCI-E slot, (which most of them have) you can run 7970. Also you will need sufficient power supply to power up the card.
However, 7970 with that CPU is not recommended as that CPU will not let the GPU to perform to its full potential. (Bottleneck).
 


I didnt say that his "system" supports it. Just the mobo. Infact I suggested him about the PSU thing.
 


amd radeon 5450 works fine..
 

OS Name Microsoft Windows 8 Pro
Version 6.2.9200 Build 9200
Other OS Description Not Available
OS Manufacturer Microsoft Corporation
System Manufacturer System manufacturer
System Model System Product Name
System Type X86-based PC
Processor Pentium(R) Dual-Core CPU E5200 @ 2.50GHz, 2500 Mhz, 2 Core(s), 2 Logical Processor(s)
BIOS Version/Date American Megatrends Inc. 0601, 10/14/2010
SMBIOS Version 2.5
Embedded Controller Version 255.255
BIOS Mode Legacy
BaseBoard Manufacturer ASUSTeK Computer INC.
BaseBoard Model Not Available
BaseBoard Name Base Board
Platform Role Desktop
Secure Boot State Unsupported
PCR7 Configuration Binding Not Possible
Boot Device \Device\HarddiskVolume1
Locale United States
Hardware Abstraction Layer Version = "6.2.9200.16442"
Time Zone India Standard Time
Installed Physical Memory (RAM) 2.00 GB
Total Physical Memory 2.00 GB
Available Physical Memory 969 MB
Total Virtual Memory 3.62 GB
Available Virtual Memory 2.04 GB
Page File Space 1.63 GB
Hyper-V - VM Monitor Mode Extensions No
Hyper-V - Second Level Address Translation Extensions No
Hyper-V - Virtualization Enabled in Firmware No
Hyper-V - Data Execution Protection Yes

 


Not this thing. The specifications on your PSU. Its om your PSU and cannot be accessed by any software.