A well-insulated pump is used to compress saturated liquid water from atmospheri

Question

A well-insulated pump is used to compress saturated liquid water from atmospheric pressure to 10 MPa in a reversible manner. Determine the outlet temperature and specific work input (KJ/kg) by the following means: Using what you know about entropy change during the process, use the property tables to find Tout & calculate specific work input using enthalpy values. Find Tout using equation 7-28, calculate specific work input using inlet specific volume and given pressure values (see equation 7-54). Calculate specific work input using average specific volume and given pressure values. NOTE: Use average specific volume based on specific volumes found from table (following approach of part a) Determine the error associated with answers to parts b & c relative to answer from part a One More NOTE: equating the expressions used to find specific work from parts a ( delta h) & b (v delta P) essentially yields the approximation for enthalpy for a compressed liquid (Eqn 3-9)

Explanation / Answer

a)

At P1 = 1 bar and sat. liquid (quality = 0) we get, s1 = 1300 J/kg-K and h1 = 418 kJ/kg, v1 = 0.00104 m3/kg, T1 = 99.6 deg C = 373 K

At P2 = 10 MPa and s2 = s1 = 1300 J/kg-K, we get h2 = 427 kJ/kg and T2 = 100 deg C, v2 = 0.00104 m3/kg

Sp. work input = h2 - h1 = 9 kJ/kg

b)

Eqn is missing to find T.

W = v1*(P2 - P1) = 0.00104*(10*10^3 - 100) = 10.296 kJ/kg

c) Average volume = (v1 + v2)/2 = 0.00104

W = 0.00104*(P2 - P1) = 10.296 kJ/kg

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