Final answer:
The new volume of the gas in the inflated weather balloon at high altitude can be calculated using the combined gas law by substituting the given initial and final pressures, initial and final temperatures (converted to Kelvin), and initial volume into the gas law formula.
Step-by-step explanation:
The problem you've outlined involves the principles of gas law, which relates to changes in pressure, volume, and temperature of a gas. According to the combined gas law, we can predict the volume of a gas when it is subjected to changes in temperature and pressure. The combined gas law equation is given by: (P1 x V1) / T1 = (P2 x V2) / T2, where P stands for pressure, V for volume, and T for temperature (in Kelvin).
To solve for the new volume (V2) at the altitude, we must convert temperatures to Kelvin: 25.7°C + 273.15 = 298.85 K; -13.7°C + 273.15 = 259.45 K. Then, rearrange the equation to solve for V2: V2 = (P1 x V1 x T2) / (P2 x T1).
Applying the values: V2 = (741 mmHg x 28.9 L x 259.45 K) / (370 mmHg x 298.85 K), now we can calculate the new volume of the balloon at altitude after performing the arithmetic.