Question

If a balloon containing 3000 L of gas at 39°C and 99 kPa rises to an altitude where the pressure is 45.5 kPa and the temperature is 16°C,

the volume of the balloon under these new conditions would be calculated using the following conversion factor ratios:

( the one I have marked, I’m not sure if that’s the answer or not )

Answer 1

`\tt =3000~L* (289)/(312)* (99)/(45.5)`

Further explanation

Given

3000 L of gas at 39°C and 99 kPa to 45.5 kPa and 16°C,

Required

the new volume

Solution

Combined with Boyle's law and Gay Lussac's law

`\tt (P_1.V_1)/(T_1)=(P_2.V_2)/(T_2)`

T₁ = 39 + 273 = 312

T₂ = 16 + 273 = 289

Input the value :

V₂ = (P₁V₁.T₂)/(P₂.T₁)

V₂ = (99 x 3000 x 289)/(45.5 x 312)

or we can write it as:

V₂ = 3000 L x (289/312) x (99/45.5)