Encoding low bitrate video source file to a higher bitrate I need to know if there will be any difference in the quality of the encoded video if the bitrate of the source file is, let's say 2000kbps and I encode it to 4000kbps. 

Any help will be much appreciated.

Thanks in advance.
Yes, the quality will be worse. But probably not perceptually. Encoding ALWAYS loses a little information, that’s why it is called lossy compression. Increasing the bitrate will only reduce the information loss. The best you can do is lossless compression, and it will look exactly like the source