Go for it and have fun! Just make sure that you have a mode C transponder above 10k.

As someone else said, doing a spiral all the way up would take up unnecessary energy and limit your climb, so go out 10 mikes and then back and forth.

A 172 should have no issue getting to 12,500 (or higher). Also, now that it's winter you will climb even easier.

You said you're young, so hypoxia shouldn't be a big issue for you at 12,500. I've done a lot of XCs in non-pressurized planes between 11000-12,500 no problem.

I find that people who have not gone that high and are from sea level are particularly susceptible to hypoxia. Doesn't have to do with being young or old, or even fit or not, even though those play factors, the conditioning is usually the biggest one. For people that cruise 10-12K without O2 day to day it's usually a non-issue, but don't discount this if it's not your normal operating procedure. Potentially big deal.

Otherwise, as people have said, a circle usually kills what little climb performance you have up high. With a lot of updrafts, you can "find" the rising air on a hot day, which is also fun.

It's nice to get up to 10K or higher on a hot day and experience the cool air.

I think the altitude record for a 150 is over 20K feet, think a lot higher actually. There is a guy claiming 19K something with a 150. Maybe that is official. I worked with a guy years ago that had one over 20. He and some buddies would regularly go to the area around Bishop, CA (at the right time of year) and ride the wave up...

That sounds awesome haha

I took a 150 to 17,500 about thirty years ago, but it wouldn't get up there by itself. It took some time, thermaling, to get it up there.

The 172 should still be climbing at its service ceiling, as that's not absolute; it's the ceiling at which the airplane still has a 100 fpm climb under original demonstration conditions (standard atmosphere).

Bring along some Beemans. And don't end up like this :D

Yep, cheap thrills... in the Summer even solo you would be lucky to get a 150 to 10K, regardless the last few thousand feet take forever, and you sure won't get there in a spiral. Many turbocharged piston planes will go much higher than advertised. The reason they are not legally permitted to do so is they would be operating outside the parameters of the flight manual. One of the biggest reasons most of the aircraft with this capability are not certified to operate at the higher altitudes is that the certification is more involved and expensive. Nevertheless, many folks have taken Cessna Turbo 210's, for example, over 30K...