Setting a default text for excerpts of a particular category

Insert the following code, in functions.php of your child theme.

function wpse_excerpt_for_specific_category( $excerpt ) {
    global $post;
    $category = 'Test'; // could be name, slug, or id
    $excerpt_text="some arbitrary text";
    if( 'post' == $post->post_type && 'publish' == $post->post_status && in_category( $category ) ) {
        $excerpt = $excerpt_text;
    }
    return $excerpt;
}
add_filter( 'get_the_excerpt', 'wpse_excerpt_for_specific_category' );

Done.