How Does Expansion Affect Internal Energy in a Monatomic Ideal Gas?

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The discussion focuses on calculating the change in internal energy for a monatomic ideal gas expanding from 100cm³ to 200cm³ at a constant pressure of 1.0 × 10⁵ Pa. The relevant equation for internal energy change is identified as ΔU = (C_v/R)PΔV, where C_v for a monatomic gas is 3/2 R. Participants clarify the application of these equations to derive the correct internal energy change. The importance of understanding the relationship between pressure, volume, and internal energy in ideal gases is emphasized. Ultimately, accurate calculations are essential for determining the thermodynamic properties of the gas during expansion.
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Homework Statement
A monatomic ideal gas expands from 100cm³ to 200cm³ at a constant
pressure of 1.0 × 10⁵ Pa. Find the change in the internal energy of the gas.
Relevant Equations
Included in my attempt at a solution
Problem Statement: A monatomic ideal gas expands from 100cm³ to 200cm³ at a constant
pressure of 1.0 × 10⁵ Pa. Find the change in the internal energy of the gas.
Relevant Equations: Included in my attempt at a solution

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You almost had it, but not quite. You had $$\Delta U=\frac{C_v}{R}P\Delta V$$And we know that, for a monatomic gas, $$C_v=\frac{3}{2}R$$Therefore,...
 
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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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