Adiabatic Compression: Understanding Internal Energy and Work in Gases

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In adiabatic compression, the change in internal energy of a gas is equal to the work done on it, assuming no heat exchange occurs. If the calculated change in internal energy is 1600J, then the work done on the gas is also 1600J. This relationship is derived from the first law of thermodynamics, which states that the change in internal energy equals the heat added to the system minus the work done by the system. Since there is no heat transfer in adiabatic processes, all the work done contributes to the change in internal energy. Therefore, the work done on the gas is indeed 1600J.
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If a gas is adiabatically compressed and the calculated change in internal energy is 1600J, is the WORK done on the gas also 1600J??
 
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Write the first principle and conclude.
 
Yes it is... Thanx for the pointer
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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