Question

A gas-filled weather balloon with a volume of 39.9 L is released at sea-level, where the prevailing conditions are 756.0 torr and 24.4°C. The balloon can expand to a maximum volume of 900 L. If the balloon rises to an altitude at which the temperature is -7.3°C and the pressure is 0.061 atm, what will the volume of the balloon be?

Answer 1

A gas-filled weather balloon with a volume of 39.9 L is released at sea-level, where the prevailing conditions are 756.0 torr and 24.4 C. The balloon can expand to a maximum volume of 900 L. If the balloon rises to an altitude at which the temperature is -7.3 C and the pressure is 0.061 atm, what will the volume of the balloon be?

Solution:

Let:

$$V1 = 39.9\,L$$ $$T1 = 24.4\,{}^{\circ}\mathrm{C} = 273.15 + 24.4 = 297.55\,K$$ $$P1 = 756\, \text{torr}$$ $$V_{\text{max}} = 900\,L$$ $$T2 = -7.3\,{}^{\circ}\mathrm{C} = 273.15 + (-7.3) = 265.85\,K$$ $$P2 = 0.061\, \text{atm} = 0.061 * 760 = 46.36\, \text{torr}$$ $$V2 - ?$$ $$\frac{P1 * V1}{T1} = \frac{P2 * V2}{T2}$$ $$V2 = \frac{P1 * V1}{T1} * \frac{T2}{P2} = \frac{P1 * V1 * T2}{P2 * T1}$$ $$V2 = \frac{756 * 39.9 * 265.85}{46.36 * 297.55} = 581.34\,L$$

Answer: 581.34 L