We are asked to calculate the temperature outside.

Calculate the volumes of the balloon:

$\overline{){\mathbf{V}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}\frac{\mathbf{1}}{\mathbf{6}}{{\mathbf{\pi d}}}^{{\mathbf{3}}}}\phantom{\rule{0ex}{0ex}}{\mathbf{V}}_{\mathbf{1}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{1}}{\mathbf{6}}\mathbf{\pi}{\mathbf{(}\mathbf{50}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{cm}\mathbf{)}}^{\mathbf{3}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{}\mathbf{65}\mathbf{,}\mathbf{449}\mathbf{.}\mathbf{85}\mathbf{}{\mathbf{cm}}^{\mathbf{3}}\phantom{\rule{0ex}{0ex}}{\mathbf{V}}_{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{1}}{\mathbf{6}}\mathbf{\pi}{\mathbf{(}\mathbf{51}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{cm}\mathbf{)}}^{\mathbf{3}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{}\mathbf{69}\mathbf{,}\mathbf{455}\mathbf{.}\mathbf{90}\mathbf{}{\mathbf{cm}}^{\mathbf{3}}$

Calculate T_{1} in K:

T_{1} = 19.0 °C +273.15 = 292.15 K

In an air-conditioned room at 19.0 C, a spherical balloon had a 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? 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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