You have several options, including:
decrease the temperature or increase the volume
Increase the pressure of the gas inside
In space, a helium-filled balloon will expand further due to the lack of air pressure outside the balloon. Eventually, the balloon will burst because the pressure from the helium inside will exceed the pressure outside.
The pressure that there would be if all the non-helium atoms and molecules were taken away.
A ballon inflates when you add helium to it for the same reason that it would inflate if you added any other gas. By Boyle's law, increasing the number of atoms of a gas to a constant space must increase the pressure of that gas. That pressure, in a balloon, must balance the force required to stretch the balloon as well as the pressure of the atmosphere pressing in on the balloon. This is not the same as the density of the displaced air. The inflated balloon would have less mass than the volume of air it displaces. This would cause the balloon to be lighter than air, and thus rise. If the elasticity of the balloon were smaller than normal, it would require more helium in a smaller volume. If the elasticity was sufficiently small, the balloon would not be lighter than air.
decrease the temperature or increase the volume
Increase the pressure of the gas inside
In space, a helium-filled balloon will expand further due to the lack of air pressure outside the balloon. Eventually, the balloon will burst because the pressure from the helium inside will exceed the pressure outside.
The pressure will increase
The pressure that there would be if all the non-helium atoms and molecules were taken away.
Increase the pressure of the gas inside
The pressure that there would be if all the non-helium atoms and molecules were taken away.
A ballon inflates when you add helium to it for the same reason that it would inflate if you added any other gas. By Boyle's law, increasing the number of atoms of a gas to a constant space must increase the pressure of that gas. That pressure, in a balloon, must balance the force required to stretch the balloon as well as the pressure of the atmosphere pressing in on the balloon. This is not the same as the density of the displaced air. The inflated balloon would have less mass than the volume of air it displaces. This would cause the balloon to be lighter than air, and thus rise. If the elasticity of the balloon were smaller than normal, it would require more helium in a smaller volume. If the elasticity was sufficiently small, the balloon would not be lighter than air.
The heat can cause the air inside the balloon to expand, increasing the pressure beyond what the balloon can handle, leading to an explosion. Helium or not, any sealed container in extreme heat can experience this pressure buildup.
Heating up a balloon will cause the air inside it to expand, which will increase the pressure inside the balloon. If the pressure exceeds the balloon's strength, it will pop or burst.
The pressure inside the balloon would be increased most at the point where you are squeezing it. Pascal's principle states that when pressure is applied to a confined fluid, that pressure is transmitted equally in all directions within the fluid. Therefore, the pressure increase would be highest at the point of application.
Without breaking the seal or puncturing the bag, there is only one thing that would increase the pressure - warming it up.