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A weather balloon containing 2.0 m³ of hydrogen gas rises from a location at which the temperature is 22°C and the pressure is 101 kPa to a location where the temperature is -39°C and the pressure is 20 kPa. If the balloon is free to expand so that the pressure of the gas inside is equal to the ambient pressure, what is the new volume of the balloon?
a. 4.0 m³
b. 6.0 m³
c. 8.0 m³
d. 10 m³
e. 12 m³

Respuesta :

Answer:

8.0 m³

Explanation:

Given:

V₁ = 2.0 m³

T₁ = 22°C = (22+273) K = 295 K

P₁ = 101 × 10³ Pa

T₂ = -39°C = (-39+273) K = 234 K

P₂ = 20 × 10³ Pa

Based on Boyle - Gay Lussac Law:

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

[tex]\frac{101\times10^3\times2.0}{295} =\frac{20\times10^3V_2}{234}[/tex]

[tex]V_2=8.0\ m^3[/tex]

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