Question

How does a physical change obey the law of conservation of mass?

Answer 1

Let's consider water.
Regardless of what form it turns into, the mass should remain the same.
It's the same H20.
Add some heat and it becomes water vapor,
cool it down a bit and it becomes ice.
if you make it just right, it becomes water again.

A chemical change would involve the one or more element(s) changing into a different solution all together.
It cannot be reversed unless you use electrolysis or some other method.