A helium-filled weather balloon has a 0.50-m radius at liftoff where air pressure is 1.00 atm and the temperature is 290 K.When airborne,the temperature is 200 K,and its radius expands to 2.00 m.What is the pressure at the airborne location?

Question

Quizplus · Accepted Answer

The ideal gas law can be expressed as: 
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the absolute temperature.

We can assume that the number of moles of helium in the balloon remains constant during the ascent. Therefore, we can express the pressure at the airborne location as:
P₂V₂ = P₁V₁(T₂/T₁)
where the subscripts ₁ and ₂ denote the liftoff and airborne conditions, respectively.

Using the given values, we have:
- V₁ = (4/3)πr₁³ = (4/3)π(0.50 m)³ = 0.524 m³
- V₂ = (4/3)πr₂³ = (4/3)π(2.00 m)³ = 33.51 m³
- T₁ = 290 K
- T₂ = 200 K

Substituting these values, we obtain:
P₂ = P₁V₁(T₂/T₁)/V₂ = (1.00 atm)(0.524 m³)(200 K/290 K)/(33.51 m³) ≈ 0.0108 atm

Therefore, the best choice is C.

A Helium-Filled Weather Balloon Has a 0