A weather balloon of known initial volume is released. The air pressures ar its initial and final altitudes are known. Why can't you find its new volume by using these known values and Boyle's law?

Answer: you cannot find its new volume by using these known values and Boyle's law because the temperature does not remain constant.

Explanation:

Boyle's law states that the volume of a fixed amount of gas, at a constant temperature, varies inversely with the pressure.

So, it is a condition that the temperature does not change.

For the wheater ballon case, as it travels through the atmosphere, the temperature at different altitudes will be different.

So, you might use other equation of states, such as the combined law, which does deal with changes in the three variables: volume, pressure, and temperature.

The mathematical formulation of Boyle's law is:

pV = constanjt ⇒ p₁ V₁ = p₂ V₂, at constant T.

The mathematical formulation of the combined law of gases is:

pV/T = constant ⇒ p₁ V₁ / T₁ = p₂ V₂ / T₂, for a fixed amount of gas, then it might work for the weather ballon (if you know the initial and end temperatures).

You cannot find the new volume by using initial volume of the weather balloon and air pressure ai its initial and final altitudes and Boyle’s law because the given values are not the same. Boyle’s law holds for the pressure and volume of the GAS at constant temperature. Here you are given the air pressure outside the weather balloon not the inside of the balloon. They have different gases and so it would not apply.