A furnace having a spherical cavity of (0.4-mathrm{m}) diameter contains a gas mixture at (1 mathrm{~atm}) and

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A furnace having a spherical cavity of \(0.4-\mathrm{m}\) diameter contains a gas mixture at \(1 \mathrm{~atm}\) and \(1400 \mathrm{~K}\). The mixture consists of \(\mathrm{CO}_{2}\) with a partial pressure of \(0.25 \mathrm{~atm}\) and nitrogen with a partial pressure of \(0.75 \mathrm{~atm}\). If the cavity wall is black, what is the cooling rate needed to maintain its temperature at \(500 \mathrm{~K}\) ?

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