If I know the maximum packet size is 1500 bytes say for Ethernet frame v2 then for example I want to transfer 1 KB over the Internet which is roughly 1024 bytes.
Will the packet be split into many packets upon sending it or will it be just one packet? If so then why would it be split when it is under the MTU size?
This question is totally hypothetical. To answer you would need to know all the hops your packet passes through, what technology each hop uses and the framesize configured (where applicable).
When it comes to internetworking, ethernet is in most cases an edge technology. Should you pass through ATM the packet will be split up in 53 byte cells of which some is overhead. Frame Relay uses negotiable PDU length. And these are just two out of many, many protocol families whose combined implementation make up 'the Internet'.
This makes the question rather difficult to answer (as you included an otherwise unspecified Internet in your path).
It should be just one packet, considering the overhead of the technology you're using for transmission.. PPP adds headers (PPPoE adds even more) if you're using VPNs or tunnels, the MTU will be further reduced. Ditto if somewhere along the way there is a hop with a reduced MTU.
You also have to consider what the data is, if it's RTP data in UDP, it might be split to reduce latency, whereas something like an FTP would likely use all the sapce available.
So both software and transmission can make a difference.
On Windows you can use Wireshark (a packet sniffer) to actually see what the packets look like and what they contain. It's a very good utility I think.
(I would just comment above but don't have the points for that yet).
