Chemistry
Chemistry
Problem
A research team is evaluating the behavior of a helium-filled weather balloon as it ascends through Earth’s atmosphere. On the launch pad the balloon occupies a volume of 25.0 L at an external pressure of 1.00 atm and a temperature of 298 K. During ascent the amount of helium remains constant while the atmospheric pressure and temperature both change. Assume the balloon gas always remains in mechanical and thermal equilibrium with the surrounding air. (a) Derive an algebraic expression for the ratio in terms of the initial and final pressures () and temperatures () for a fixed quantity of gas in a flexible container. (b) Given that both and , explain qualitatively how these simultaneous changes compete to influence the balloon’s volume. Indicate which effect you predict will dominate for typical tropospheric conditions and justify your reasoning with the expression from part (a). (c) If the external pressure continues to decrease while the temperature stabilizes at a constant value, describe qualitatively what will happen to the balloon’s volume and why. Include a statement about any limiting factors that might prevent indefinite volume expansion.Intuitive explanation
The key here is recognizing that helium behaves as an ideal gas, so you can use the combined gas law to track how volume changes as the balloon rises. Since the amount of gas is fixed and the balloon stays in equilibrium with its surroundings, pressure and temperature are no longer independent—they're both set by the atmosphere at each altitude. Your job is to connect initial conditions to final conditions using , which lets you predict the balloon's volume at any point in the atmosphere.
Intuitive explanation
The key here is recognizing that helium behaves as an ideal gas, so you can use the combined gas law to track how volume changes as the balloon rises. Since the amount of gas is fixed and the balloon stays in equilibrium with its surroundings, pressure and temperature are no longer independent—they're both set by the atmosphere at each altitude. Your job is to connect initial conditions to final conditions using , which lets you predict the balloon's volume at any point in the atmosphere.