Every Application Pool is (normally) associated with one worker process named w3wp.exe
If the application pool becomes unresponsive, you can kill it. It doesn't affect any of the other application pools or IIS over all.
All sites using that application pool will be affected, but they may be already.
The application pool may start up again automatically, but you should check that.
If you have multiple application pools, you will see multiple w3wp.exe
so you need to kill the correct one.
On Server 2012+, open task manager and click on the Details
tab. right click on the column headers Select columns
and tick Command line
.
Now look at the w3wp.exe processes and find the one that has your application pool name in its command line. Right click that process and End Task
I don't think in older versions of Windows you can see the command line.
You can use third party tools like Process Explorer or Process Hacker, the second one can try many ways to kill a process.