The Tonga Trench in the Pacific Ocean is 36,000 feet deep. Assuming that sea water has an average density of $1.04 \mathrm {~g} / \mathrm { cm } ^ { 3 }$ calculate the absolute (total) pressure at the bottom of the trench in atmospheres. $\left( 1.00 \mathrm { in } = 2.54 \mathrm {~cm} , 1.00 \mathrm {~atm} = 1.01 \times 10 ^ { 5 } \mathrm {~Pa} \right)$

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To calculate the absolute pressure at the bottom of the Tonga Trench, we first convert the depth from feet to cm (since the density is given in g/cm^3), then calculate the pressure in Pascals using the formula for pressure due to a column of fluid $P = \rho gh$, and finally convert that pressure to atmospheres.1. Convert depth to cm: $36,000 \text{ feet} \times 12 \text{ inches/foot} \times 2.54 \text{ cm/inch} = 1,097,280 \text{ cm}$.2. Calculate pressure in Pascals: $P = \rho gh = 1.04 \text{ g/cm}^3 \times 9.8 \text{ m/s}^2 \times 1,097,280 \text{ cm} = 1.04 \times 10^3 \text{ kg/m}^3 \times 9.8 \text{ m/s}^2 \times 10,972.8 \text{ m} = 1.12 \times 10^8 \text{ Pa}$.3. Convert pressure to atmospheres: $1.12 \times 10^8 \text{ Pa} / (1.01 \times 10^5 \text{ Pa/atm}) \approx 1.1 \times 10^3 \text{ atm}$.Therefore, the absolute pressure at the bottom of the Tonga Trench is approximately $1.1 \times 10^3 \text{ atm}$.

The Tonga Trench in the Pacific Ocean Is 36,000 Feet 1.04 g/cm31.04 \mathrm {~g} / \mathrm { cm } ^ { 3 }1.04 g/cm3

The Tonga Trench in the Pacific Ocean Is 36,000 Feet $1.04 \mathrm {~g} / \mathrm { cm } ^ { 3 }$