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A helium-filled weather balloon has a 0.90 m radius at liftoff where air pressure is 1.0 atm and the temperature is 298 K. When airborne, the temperature is 210 K, and its radius expands to 3.0 m. What is the pressure at the airborne location

Respuesta :

Answer:

0.019 atm

Explanation:

Assume ideal gas, so PV/T is constant where P is pressure, V is volume and a product of radius R cubed and a constant C, T is the temperature

[tex]\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}[/tex]

[tex]P_2 = P_1\frac{V_1}{V_2}\frac{T_2}{T_1}[/tex]

[tex]P_2 = P_1\frac{CR_1^3}{CR_2^3}\frac{T_2}{T_1}[/tex]

[tex]P_2 = P_1\left(\frac{R_1^3}{R_2^3}\right)^3\frac{T_2}{T_1}[/tex]

[tex]P_2 = 1\left(\frac{0.9}{3}\right)^3\frac{210}{298}[/tex]

[tex]P_2 = 0.3^3*0.7 = 0.019 atm[/tex]