Append class to posts page

In your theme’s functions file, use the body_class filter to add new classes:

function wpse_282694_body_class( $classes ) {
    if ( is_home() ) {
        $classes[] = 'blog';
    }

    return $classes;
}
add_filter( 'body_class', 'wpse_282694_body_class' );

If your category archives, tag archives, date archives and search results also need the same styling, which is fairly commin, check for each of them like so:

if ( is_home() || is_date() || is_tag() || is_category() || is_search() ) {}

Note that I didn’t use is_archive(), because that would also affect any custom post types you might be using.