Soru

A meteorological balloon filled with $0.50\text{ kg}$ of helium gas is launched at sea level, where the atmospheric pressure is $1.01 \times 10^5\text{ Pa}$ and the ambient temperature is $27^\circ\text{C}$. The balloon ascends to a high altitude where the external ambient pressure decreases to $4.00 \times 10^4\text{ Pa}$ and the ambient temperature drops to $-23^\circ\text{C}$. As the balloon expands, its elastic membrane exerts an additional pressure, causing the internal gas pressure to be $20\%$ higher than the surrounding ambient pressure. Assuming helium behaves as an ideal gas with a molar mass of $4.0\text{ g/mol}$ and the molar gas constant $R = 8.31\text{ J mol}^{-1}\text{K}^{-1}$, calculate the final volume of helium gas inside the balloon at this altitude in $\text{m}^3$.