Multiple servers?

I set up Thunderbird Portable with my university's incoming mail servers and my outgoing mail server as my home internet provider. At home, I can check and send mail without a problem, but at the university I can receive but not send it. When I try to send mail from the university I get this message:

"An error occurred while sending mail. The mail server responded: #5.1.0 Address rejected... Please verify that your email address is correct in your Mail preferences and try again."

How can this be resolved? Do I have to change the outgoing server depdending on my location?

This is my first post, if this has been addressed elsewhere please direct me to that thread.

Thank you for your help.