You can always wrap the child elements of #first and save height height of the wrapper as a variable. This might not be the prettiest or most efficient answer, but it does the trick.
Here's a fiddle where I included a reset.
but for your purposes, here's the meat & potatoes:
$(function(){
//wrap everything inside #first
$('#first').children().wrapAll('<div class="wrapper"></div>');
//get the height of the wrapper
var expandedHeight = $('.wrapper').height();
//get the height of first (set to 200px however you choose)
var collapsedHeight = $('#first').height();
//when you click the element of your choice (a button in my case) #first will animate to height auto
$('button').click(function(){
$("#first").animate({
height: expandedHeight
})
});
});?