This article has been migrated to its new home here: https://benperk.github.io/msdn/2012/2012-06-using-powershell-3-0-on-windows-8-to-find-the-process-id-pid-of-an-application-pool.html
With the release of Windows 8 Server comes a new version of PowerShell. You can check which version of PowerShell you are using by executing the command show in Figure 1.
Figure 1, Which version of PowerShell am I using
To get a list of application pools existing on the web server enter the following shown in Figure 2.
Figure 2, How to list the application pools using PowerShell 3.0
To get the process id of the application pool, execute the command shown in Figure 3.
Figure 3, how to get the process id (PID) of an application pool using PowerShell 3.0
Then, if required you can use that PID in combination with ProcDump to create a memory dump for analysis.