Potential Problem of Using Session Variables?

Hi everyone, I'm wondering if logging into the same web app by the same person multiple times will cause a problem when using session variables. In other words if multiple instances of the same app are opened by the same user, will the app get confused as to which session variable is used. For an example, suppose User1 opens an app and stores the value of "25" into a session variable Session["myValue"].
Then he opens the same app in another window and inserts the value "50" into Session["myValue"] while keeping the first instance of the same app opened. If he then displays the value of this session variable in the second instance of this app which he opened just a second ago, will it display 25 or will it display 50? Thanks in advance for your input.