Loading a Cisco IOS on Flash

Sometimes with my job I am required to put an IOS on a piece of flash. Normally it is an IOS for a Cisco 2811 router. I usually boot up the 2811, remove the flash in the router, then put in the new piece of flash and copy the IOS from the TFTP server to the flash. Here is my question. Can I copy an IOS for a 3800 router from the TFTP server to the piece of flash on the 2811 router; or do I have to use a 3800 router? This is just to copy an IOS to the flash memory only.