Since the balloon is sealed, the number of helium atoms it contains doesn’t change when you cool it or warm it. However, that doesn’t mean that the balloon’s size is fixed. What you are observing here is the relationship between three important properties of a trapped gas: its temperature, its pressure, and its volume. As you cool the balloon, its volume shrinks so as to keep its internal pressure in balance with the surrounding air pressure. When you later heat the balloon, its volume increases to maintain this same pressure balance.
The pressure that a fixed quantity of gas exerts on its container is determined by two things: (1) that gas’s temperature and (2) how densely packed its particles are. Since temperature is related to speed of motion in the gas particles, the particles in a hotter gas hit their container harder and more often than those in a cooler gas and they exert more pressure on that container. Similarly, the particles in a more densely packed gas hit each unit of container surface more often than those in a more dilute gas and thus exert more pressure. Overall, the pressure that a fixed quantity of gas exerts on its container is proportional to the gas’s temperature (more on how to measure this temperature in a minute) and to its packing density.
When you take your helium balloon outside and it cools off, the pressure in the balloon begins to drop as its gas atoms slow down. Because the balloon is surrounded by air at atmospheric pressure, the balloon begins to experience a pressure imbalance that crushes the balloon inward. As the balloon shrinks from this imbalance and its volume decreases, the helium atoms inside it become more tightly packed. That increasing packing density raises the helium’s pressure and eventually stops the balloon from shrinking further. Thus for a given decrease in gas temperature, there is a specific decrease in balloon volume that balances it and allows the balloon’s internal pressure to equal the atmospheric pressure surrounding the balloon.
When you later return the chilled balloon to the warm indoors, its trapped helium atoms warm up and become more effective at producing pressure. They push the balloon’s skin outward against the surrounding air pressure and the balloon expands. As it expands, its atoms spread out and become more dilute. They become less effective at producing pressure and the balloon again reaches a specific size at which the balloon’s internal pressure exactly balances the atmospheric pressure surrounding the balloon.
Finally, a word about temperature and gas properties. In an “ideal gas”—a gas in which the particles don’t stick to one another at all—the pressure is exactly proportional to the temperature times the packing density of the particles. Helium is nearly an ideal gas, so it follows this behavior beautifully. Since the packing density of a trapped gas is inversely proportional to that gas’s volume, the temperature of the gas is proportional to the gas’s pressure times its volume. In a balloon, the compressing effects of the surrounding air makes sure that the balloon’s internal pressure stays constant. So as the balloon’s temperature decreases, so does the balloon’s volume. One is exactly proportional to the other.
But the temperature we are talking about here is measured in what is known as an “absolute temperature scale”—a scale in which the zero of temperature is the true zero: absolute zero—the temperature at which all thermal energy has been removed from the system (–459o F or –273o C). The standard absolute temperature scale is the Kelvin scale or K. Room temperature is about 300 K. If you were to take your balloon into a 150 K environment (about –190o F), it would shrink to exactly half its original volume.
Answered by Lou A. Bloomfield of the University of Virginia