Check My Solution for Second Problem (w,q)

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The discussion revolves around a request for validation of a solution to a thermodynamics problem involving work (w) and heat (q) per kilogram. The poster highlights the complexity of their work, which addresses simultaneous changes in kinetic and thermal energy between two conditions. Feedback indicates that while the solution may be difficult to read, it appears correct upon review. The poster provides a link to a resource on steam generation thermodynamics for further context. Overall, the focus is on ensuring the accuracy of the proposed solution in thermodynamic analysis.
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Homework Statement
In the turbine steam changes its specific enthalpy and velocity from (3450) kJ/kg and 85 m/s at the inlet to (2630) kJ/kg and 190 m/s at the outlet. (A) Determine the power generated per 1 kg of the steam if the process is adiabatic. (B) Determine also the power generated if the heat lost to surroundings is 10kJ per 1kg of steam flowing through the turbine. Neglect change in potential energy.
Relevant Equations
Balance of Energy
Hi there again. I have a second problem for which I don't have an answer to compare with, hence I'm kindly asking someone to check the solution of mine. lower case w and q are the work and heat per 1kg respectively, and w's with a vector are of course the velocities at the inlet and at the outlet.
Turbine First Law.jpg
 
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Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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