Decades ago, it was thought that huge herbivorous dinosaurs such as Apatosaurus

Question

Decades ago, it was thought that huge herbivorous dinosaurs such as Apatosaurus and Brachiosaurus habitually walked on the bottom of lakes, extending their long necks up to the surface to breathe. Brachiosaurus had its nostrils on the top of its head. In 1977, Knut Schmidt-Nielsen pointed out that breathing would be too much work for such a creature. For a simple model, consider a sample consisting of 14.0 L of air at absolute pressure 2.0 atm, with density 2.40 kg/m^3, located at the surface of a freshwater lake. Find the work required to transport it to a depth of 12.5 m, with its temperature, volume, and pressure remaning constant. This energy investment is greater than the energy that can be obtained by metabolism of food with the oxygen in that quantity of air.express answer in kj

Explanation / Answer

volume V=14 litres or 14/1000 m^3 ;
P=2 atm or 2*10^5 pa ;

(air)=2.40 kg/m^3 ; (water)=1000 kg/m^3 ;

work done =work done by buoyancy - loss in potential energy = (water)*0.014*g*h - (air)*0.014*g*h ;

=0.014*9.81*12.5*(1000-2.4)=1712.63 N

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