jQuery changing css class to div

Yep, easily.

$("#mydiv").attr("class", "second");

$(".first").addClass("second");

If you'd like to add it on an event, you can do so easily as well. An example with the click event:

$(".first").click(function() {
    $(this).addClass("second");
});

You can add and remove classes with jQuery like so:

$(".first").addClass("second")
// remove a class
$(".first").removeClass("second")

By the way you can set multiple classes in your markup right away separated with a whitespace

<div class="second first"></div>

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