Calculating h & u for values not on tables (Thermodynamics)

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To find thermodynamic values not listed in tables, interpolation is the recommended method, assuming the function behaves linearly between known values. When dealing with properties like enthalpy or internal energy, use the surrounding values from the tables to calculate a weighted average. This approach is essential for accurately determining properties for substances at specific pressures and temperatures. The discussion emphasizes the importance of clear communication regarding the values being referenced from the tables. Understanding interpolation techniques is crucial for solving related homework problems effectively.
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Hi, most of my thermodynamics class we have been looking up enthalpy on tables when the pressure and temperature is provided. For some homework questions, the values are not on the tables, but fall in between them. What is the correct approach to finding these when the quality is not provided? For example:

Which has the capability to produce the most work in
a closed system—1 kg of steam at 800 kPa and 180°C or 1 kg
of R-134a at 800 kPa and 180°C? Take T 0 = 25°C and PQ =
100 kPa. Answers-. 623 kJ, 5.0 kj


u = 2594 . 7 kJ/kg
P = 800 kPa
v = 0 . 24720 m /kg
T = 180 ° C
s = 6 . 7155 kJ/kg ⋅ K


u 0 ≅ u f @ 25 ° C = 104 . 83 kJ/kg


v 0 ≅ v f @ 25 ° C = 0 . 001003 m /kg
P 0 = 100 kPa
s 0 ≅ s f @ 25 ° C = 0 . 3672 kJ/kg ⋅ K
T 0 = 25 ° C

(Edited in correct values)

What is the correct approach to get here?
The textbook I am using is Thermodynamics 7e (cengal)

Thanks!
 
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Can't interpret the example without being told what values are in the tables and what values you are trying to look up. (Try not to assume anyone wanting to respond to you has the same book.)
As a general matter, there's interpolation and extrapolation. If the values you have lie between those in the tables then it would be usual to assume (in the absence of glaring evidence to the contrary) that the function is about linear in between adjacent the values in the tables. So you can just do a weighted average. Do you know how to do that?
 
Look up interpolation. That's how you find values that are in between.
 
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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