An airtight box, having a lid of area 80 cm², is partially evacuated. Atmospheric pressure is 1.01 *10⁵ Pa. A force of 108 lb is required to pull the lid off the box. The pressure in the box was: A) 2.60 * 10⁴ Pa B) 6.35 * 10⁴ Pa C) 7.50 * 10⁴ Pa D) 1.38 * 10⁵ Pa E) 1.76 * 10⁵ Pa

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Quizplus · Accepted Answer

The pressure difference between the inside and outside of the box is equal to the force required to pull the lid off divided by the area of the lid. Therefore, the pressure in the box is:$$P = \frac{F}{A} = \frac{108 	ext{ lb}}{80 	ext{ cm}^2} = 1.35 	imes 10^5 	ext{ Pa}$$Converting to Pascals:$$P = 1.35 	imes 10^5 	ext{ Pa} 	imes \frac{1 	ext{ atm}}{1.013 	imes 10^5 	ext{ Pa}} = 1.33 	ext{ atm}$$Therefore, the pressure in the box is closest to 1.38 atm, which is choice A.

An Airtight Box, Having a Lid of Area 80 Cm2

An Airtight Box, Having a Lid of Area 80 Cm²