Apparently adding text without HTML tags fails when you use XMLWorker. This is a known bug. For now a workaround would be to check whether a string has HTML elements or not and if it doesn't, you could wrap it in a paragraph tag.
I adjusted your sample to make it work:
List<String> strList=new ArrayList<String>();
String first="<p>First Page</p>";
String second="<p>second Page</p>";
strList.add(first);
strList.add(second);
for(String string:strList)
{
doc.newPage();
// I just prefer StringReaders over ByteArrayInputStreams
worker.parseXHtml(pdfWriter, doc, new StringReader(string));
}
Also, for future reference, your code threw an Exception, it would be best if you would provide any thrown exceptions in future questions.