Why when copying to an external drive the progress window is not correct

I would suppose you are using Nautilus as your file manager and if so there are long-standing bugs about this. Too numinous to mention effecting Mint, Fedora, Red Hat and all the like. Ubuntu is not without this same issue.

Some suggest turning off thumbnail view helps. Others put their hopes in the "newest kernel" but this still exists.

The problem = Starts off fast, then goes slower This is because when mounted with async it will write to the cache, when the cache is full you see the "Real" write speed.

The work around seems to be sudo cp /filetobecopied /dev/nameofdevice

another posted here says that "copying in chunks" works. Unconfirmed on my part.

This is also a nice answer with a solution: https://unix.stackexchange.com/a/181236 It says:

The reason it happens that way is that the program says "write this data" and the linux kernel copies it into a memory buffer that is queued to go to disk, and then says "ok, done". So the program thinks it has copied everything. Then the program closes the file, but suddenly the kernel makes it wait while that buffer is pushed out to disk.

So, unfortunately the program can't tell you how long it will take to flush the buffer because it doesn't know.

If you want to try some power-user tricks, you can reduce the size of the buffer that Linux uses by setting /proc/sys/vm/dirty_bytes to something like 15728640 (15 MB). This means the application can't get more than 15MB ahead of its actual progress.

A side effect is that your computer might have lower data-writing throughput with this setting, but on the whole, I find it helpful to see that a program is running a long time while it writes lots of data vs. the confusion of having a program appear to be done with its job but the system lagging badly as the kernel does the actual work. Setting dirty_bytes to a reasonably small value can also help prevent your system from becoming unresponsive when you're low on free memory and run a program that suddenly writes lots of data.

But, don't set it too small! I use 15MB as a rough estimate that the kernel can flush the buffer to a normal hard drive in 1/4 of a second or less. It keeps my system from feeling "laggy".