IO#inspect will return string that include the descriptor number.

Test Script:
{{{
require 'test/unit/assertions.rb'
include Test::Unit::Assertions

r, w = IO.pipe
w.close
assert_match(/#<IO:fd \d+>/,   r.inspect)
assert_equal("#<IO:(closed)>", w.inspect)

f = File.open("/tmp/test.txt", "w")
assert_equal("#<File:/tmp/test.txt>", f.inspect)
f.close
assert_equal("#<File:/tmp/test.txt (closed)>", f.inspect)

puts :ok
}}}

io.c

@@ -870,19 +870,32 @@ static VALUE
 rb_io_inspect(VALUE io, SEL sel)
 {
     rb_io_t *io_struct = ExtractIOStruct(io);
-    if (io_struct == NULL || io_struct->path == 0) {
+    if (io_struct == NULL) {
         return rb_any_to_s(io);
     }
 
     VALUE str = rb_str_new2("#<");
     rb_str_cat2(str, rb_obj_classname(io));
     rb_str_cat2(str, ":");
-    rb_str_concat(str, io_struct->path);
-    if (!rb_io_is_open(io_struct)) {
-	rb_str_cat2(str, " (closed)>");
+    if (io_struct->path == 0) {
+	if (!rb_io_is_open(io_struct)) {
+	    rb_str_cat2(str, "(closed)>");
+	}
+	else {
+	    char fd_desc[4+sizeof(int)*3];
+	    snprintf(fd_desc, sizeof(fd_desc), "fd %d", io_struct->fd);
+	    rb_str_cat2(str, fd_desc);
+	    rb_str_cat2(str, ">");
+	}
     }
     else {
-	rb_str_cat2(str, ">");
+	rb_str_concat(str, io_struct->path);
+	if (!rb_io_is_open(io_struct)) {
+	    rb_str_cat2(str, " (closed)>");
+	}
+	else {
+	    rb_str_cat2(str, ">");
+	}
     }
     return str;
 }