Is there any free .net library to convert word to pdf in asp.net for a C# application?
According to your question I think you can use Free.NET Word Library. It designed for developers to create, read, write, convert and print Word document files from any .NET platform. You can download it by using this link.
You can try Syncfusion .NET Word library (Essential DocIO) to create, read, manipulate and convert Word documents programmatically without Microsoft Word or other dependencies in your machine. It offers the Word to PDF conversion ability as well.
More Word Examples: https://ej2.syncfusion.com/aspnetmvc/DocIO/UpdateFields#/material
The whole suite of controls is available for free (commercial applications also) through the community license program if you qualify. The community license is the full product with no limitations or watermarks.
Note: I work for Syncfusion.