In an air-conditioned room at 19.0 ∘C, a spherical balloon had the diameter of 50.0 cm. When taken outside on a hot summer day, the balloon expanded to 51.0 cm in diameter. What was the temperature outside in degrees Celsius?

Assume that the balloon is a perfect sphere and that the pressure and number of moles of air molecules remains the same.

Question

Chemistry

Sweet Tea

29 July, 17:11

In an air-conditioned room at 19.0 ∘C, a spherical balloon had the diameter of 50.0 cm. When taken outside on a hot summer day, the balloon expanded to 51.0 cm in diameter. What was the temperature outside in degrees Celsius?

Assume that the balloon is a perfect sphere and that the pressure and number of moles of air molecules remains the same.

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Answers (1)

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Danielle Wiggins · Answer 1

20.2 °C

Explanation:

When the pressure and number of moles are constant, Charles's law may be used to solve for temperature:

T₁/V₁ = T₂/V₂ >> T₂ = T₁ (V₂/V₁)

Expressions for the volumes can be substituted and simplified:

T₂ = T₁ (V₂/V₁) = T₁ (4/3πr₂³/4/3πr₁³) = T₁ (r₂³/r₁³)

Substituting in values in the equation (where the radius r is half of the diameter) gives:

T₂ = T₁ (r₂³/r₁³) = (19.0°C) x ((51.0cm/2) ³ / (50.0cm/2) ³) = 20.2 °C