A weather balloon contains 12.0 m³ of hydrogen gas when the balloon is released from a location at which the temperature is 22.0°C and the pressure is 101 kPa.The balloon rises to a location where the temperature is -30.0°C and the pressure is 20.0 kPa.If the balloon is free to expand so that the pressure of the gas inside is equal to the ambient pressure,what is the new volume of the balloon? Assume that in both cases the hydrogen gas is in thermal equilibrium with the outside air. A) 14.0 m³ B) 2.38 m³ C) 49.9 m³ D) 82.6 m³ E) 4.16 m³

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Quizplus · Accepted Answer

To find the new volume of the balloon, we can use the combined gas law, which is $P_1V_1/T_1 = P_2V_2/T_2$, where $P$ is pressure, $V$ is volume, and $T$ is temperature in Kelvin. First, convert temperatures to Kelvin: $T_1 = 22.0°C + 273.15 = 295.15 K$ and $T_2 = -30.0°C + 273.15 = 243.15 K$. Then, solve for $V_2$: $V_2 = V_1 \times (P_1/P_2) \times (T_2/T_1)$. Substituting the given values: $V_2 = 12.0 \times (101/20) \times (243.15/295.15)$, which calculates to approximately $49.9 m^3$, making option C correct.

A Weather Balloon Contains 12