Thermodynamics Change in Internal Energy?

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The discussion centers on a thermodynamics problem involving a closed, rigid tank containing water transitioning from a two-phase liquid-vapor mixture at 70°C to saturated vapor at 120°C. The key equations used include the internal energy change formula ΔU = Q - W, with work (W) being zero due to the rigid tank. The initial internal energy (u1) is calculated by combining the specific internal energies of the saturated liquid and vapor, while the final internal energy (u2) only considers the saturated vapor. The participant initially miscalculated the heat transfer (Q) but later acknowledged the error. The correct heat transfer value is sought from the provided options.
Ricardeo Xavier
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Homework Statement


A closed, rigid tank contains 2 kg of water, initially a two phase liquid–vapor mixture at T1 = 70°C. Heat transfer occurs until the tank contains only saturated vapor at T2 = 120C.
Determine the heat transfer for the process, in kJ.
answer choices:
3701kJ
119.4kJ
4835kJ
1558kJ

Homework Equations


Steam Tables
ΔU=Q-W(W=0)

The Attempt at a Solution


Since we know T1, we can use the tables to identify the specific internal energy of saturated liquid and gas and add them together to find u1. We can also do the same with T2 but neglecting the specific internal energy of fluid since it is only a saturated vapor at this point. Subtract u2 from u1 then multiply by the mass. Since it is a rigid tank we can also neglect work done. Here is my work:
Q=m(u2-u1)
Q=2kg(2529.3kJ/kg - (292.95kJ/kg+2469.6kJ/kg))
Q=-466.5kJ (this answer is not given as one of the choices so i am assuming that it is wrong)
 
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Nevermind i figured it out. I did this completely wrong
 
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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