Thats about what my daily commute is. It can be a real workout or a relaxing cruise depending on how heavy your setup is and how fast you want to go. Have you ever ridden a road bike? If you can get away with traveling light on some thinner tires you'll be able to make it in 20 minutes without even breaking a sweat. A hard effort on a mountain bike (especially if you have dirt tires) might get you 20 kph while a light effort on a road bike might get you close to 30 kph. The speed advantage doubles down too when you find that you are putting in less effort and getting more wind, staying nice and cool the whole way.

I'd at least suggest some hard rubber road oriented tires, depending on how often you are going to commute vs. how much dirt you ride. It will make all the difference. Really, you could take ten of the extra 40 minutes you'll gain by biking every day to change your tires...

Also, yeah. strongly suggest a rack for your bag and a small towel, along with avoiding riding in uniform if possible. Even just wearing super light shorts and a shirt then throwing the uniform on over it and you'll have less of a sweat issue.