Question

A piston-cylinder assembly contains water vapor, initially at 10 bar and 360 deg C. The water undergoes a process where pv=constant until it reaches a final pressure of 1.5 bar. (a) Draw the process in p-v and T-s diagrams clearly labeling the states and the direction of the process. (b) Write the engineering model (c) Determine the energy transfers by work and heat, in kJ/kg and indicate their direction (in or out) (d) Determine the entropy production if the temperature at the boundary is Tb=630 K and comment on the nature of the process (reversible, irreversible, or impossible)

Answer 1

a) Check the attached file

b)
`\phi = U_(2) - U_(1)`

c)Energy transfer by work,
`W = 545 kJ/kg`

Energy transfer by heat, E = 543 kJ/kg

d)The entropy production,
`\triangle S = 0.0015 kJ/kg-K`

The process is irreversible

Step-by-step explanation:

Initial Pressure, P₁ = 10 bar

Initial temperature, T₁ = 360⁰ C

Final Pressure, P₂ = 1.5 bar

At P₁ = 10 bar and T₁ = 360°C

Getting the other parameters from the steam table:

V₁ = 0.28736 m³/kg, U₁ = 2892.05 kJ/kg, h₁ = 379.09 kJ/kg, S₁ = 7.3366 kJ/K

Using Boyle's law, to get V₂

P₁ V₁ = P₂V₂

10 * 0.28736 * = 1.5 * V₂

V₂ = 1.9157 m³/kg

At P₂ = 1.5 bar and V₂ = 1.9157 m³/kg

U₂ = 2890 kJ/Kg, h₂ = 3180 kJ/kg, S₂ = 8.2 kJ/K, T₂ = 351° C

a) Check the attached file for the P-V and T-S diagrams

b) Write the engineering model

The system described is a closed system

`\phi = \triangle U + W\\\phi = U_(2) - U_(1)`

c) Energy transfer by work and heat

Energy transform by work

`W = P_(1) V_(1)ln((P_(1) )/(P_(2) ) )\\ W = (10*0.287)ln((10)/(1.5) )\\W = 545 kJ/kg`

Energy transform by heat

E = ( U₂ - U₁) + w

E = (2890 - 2892.05) + 545

E = 543 kJ

d)

`(\triangle S)_(123) = S_(2) - S_(1)\\(\triangle S)_(123) = 8.2 - 7.3366\\(\triangle S)_(123) = 0.8634 kJ/kg-K\\`

`( \triangle S)_(b) = (-q)/(T_(b) )\\( \triangle S)_(b) = (-543)/(630 )\\( \triangle S)_(b) = -0.8619 kJ/kg-K`

`\triangle S = (\triangle S)_(sys) + (\triangle S)_(b)\\\triangle S = 0.8634 - 0.8619\\\triangle S = 0.0015 kJ/kg-K`

The process is irreversible since ΔS > 0