jQuery - Auto Scroll to bottom of a Chat Box

HTML

<div>
    <p>alskdjg;j ;jhe ;he fkh</p>
    <p>alskdjg;j ;jhe ;he fkh</p>
    <p>alskdjg;j ;jhe ;he fkh</p>
    <p>alskdjg;j ;jhe ;he fkh</p>
    <p>alskdjg;j ;jhe ;he fkh</p>
    <p>last one</p>
</div>

CSS

div {
    height: 100px;
    background: aqua;
    overflow: auto;
}

JavaScript

var height = 0;
$('div p').each(function(i, value){
    height += parseInt($(this).height());
});

height += '';

$('div').animate({scrollTop: height});