Question

Question 18

2 Points

Humpback whales can dive to 176 m depth where the pressure is 1.78 MPa. Assuming that the whales body temperature is constant (36.40 ^oC), what volume will the whales lungs now have? 2,048.7636 L (Assume that the pressure at the surface is 1.000 atm or 101.3 kPa and the initial volume of the lungs is 3.600 x 10³ L, give your answer to 3 significant figures, do not use scientific notation)

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Answer 1

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According to Boyle's law, we know that, at constant temperature, pressure is inversely proportional to the volume of the gas.

Here, given that, temperature is constant.

Initial pressure, $P_{i}=101.3\;kPa=101300\;Pa$

Final pressure, $P_{f}=1.78\times10^{6}\;Pa$

Initial volume, $V_{i}=3600\;L$

Therefore final volume is given by,

$V_{f}=\frac{P_{i}V_{i}}{P_{f}}=\frac{3600\;L\times 101300\;Pa}{1.78\times10^{6}\;Pa}$

$\therefore V_{f}=204.88\;L$

Rounding to 3 significant figures,

$\mathbf{\therefore V_{f}=205\;L}$

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