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12 January, 22:32

A piston with stops containing water goes through an expansion process through the addition of heat. State 1 the pressure is 200 kPa and the volume is 2 m3. After half of the heat has been delivered the piston hits the stops corresponding to a volume of 5 m3. After all the heat has been delivered, state 2, the pressure is 1000 kPa with the piston resting on the stops. What is the work?

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  1. 12 January, 22:53
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    The work will be "600 kJ/kg".

    Explanation:

    (1-a) ⇒ Constant Pressure

    (a-2) ⇒ Constant Volume

    The given values are:

    In state 1,

    Pressure, P₁ = 200 kPa

    Volume, V₁ = 2m³

    In state 2,

    Pressure, P₂ = 1000 kPa

    Volume, V₁ = 5m³

    Now,

    In process (1-a), work will be:

    ⇒ W₁₋ₐ = P₁ (Vₐ - V₁)

    On putting the values, we get

    ⇒ W₁₋ₐ = 200 (5-2)

    ⇒ = 200 (3)

    ⇒ = 600 kJ/kg

    In process (a-2), work will be:

    ⇒ Wₐ₋₂ = 0

    ∴ (The change in the volume will be zero.)

    So,

    ⇒ Total work = (W₁₋ₐ) + (Wₐ₋₂)

    ⇒ = 600 + 0

    ⇒ = 600 kJ/kg
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