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Rumpelstiltzkin

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A 0.5m3 rigid tank contains refrigerant-134a initially at 200kPa and 40% quality. Heat is now transferred to the refrigerant until the pressure reaches 800kPa. Determine (a) the mass of the refrigerant in the tank and (b) the amount of heat transferred. Also, show the process on a P-υ diagram with respect to saturation lines.

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The solution for this question was already released, and I know the working to do it, but I can't understand the concept for part (b). In the solution, the amount of heat transfer was given as Q = (mass) * (change in specific internal energy, u).

I'm confused: Why can't we use change in enthalpy, h? Doesn't the change in enthalpy also mean heat transfer? I know it has something to do with the volume being constant ("rigid tank"), but I don't see how exactly.

Would someone care to explain what's the difference between these two properties?

Thanks.