Solve the problem in picture. Gas inside a piston-cylinder assembly as shown bel

Question

Solve the problem in picture.

Gas inside a piston-cylinder assembly as shown below has a mass of 2 kg. The gas undergoes a compression from state 1, where the specific internal energy is 2250 kJ/kg to state 2, where the specific internal energy is 1975 kJ/kg. During the process, there is a heat transfer to the system with magnitude of 80 kJ. In addition, the piston decreases the system volume by 0.23 m^3. If pressure remains constant throughout the process at 325 kPa, how much energy is transferred to a paddle wheel inside the cylinder by work? (Note: there are two components of work -2 locations where work crosses the system boundary)

Explanation / Answer

Mass, m = 2kg

u1 = 2250 KJ/kg

u2 = 1975 KJ/kg

Q12 = 80 KJ

V2 - V1 = -0.23 m3

P = 325 KPa

Boundary work, Wb= P (V2- V1) = - 325 X 0.23 = -74.75 KJ

Applying energy conservation, we get

Q12 = m (u2 - u1) + Wb + Wp

80 = 2( 1975 - 2250) -74.75 + Wp

work transferred to paddle wheel, Wp = 704.75 KJ....answer

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