1 kg of water that is initially 90oC with a quality of 10 percent occupies a spring-loaded piston-cylinder device. At this state, a linear spring is touching the piston and exerting no force on it. The device is now heated to compress the spring until the pressure rises to 800 kPa and the temperature is 250oC. Determine the total work produced during this process, in kJ.

The total work produced during this process is 24.43 KJ.

Explanation:

Here we have from steam tables at 90 °C  

P₁ = 0.701824 bar = 70.1824 Pa

Since the quality is 10 %, this gives the fraction of liquid present in the steam, hence we have the specific volume given by

v₁ = 0.00103594 + 0.1 × (2.35915 - 0.00103594) = 0.236847346 m³/kg

When the steam is then heated, we have from the super heated steam tables at T₂ = 250 °C and P₂ = 800 kPa

v₂ =0.293 m³/kg

Therefore the work done is given by

Area under the PV curve, which is

Average pressure × Change in volume

= 24.43 KJ.

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