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15 February, 19:27

The gauge pressure inside a vessel is - 40kPa, at an elevation of 5000m. a) What is the absolute pressure? b) At this elevation, what temperature does water boil?

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  1. 15 February, 19:44
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    a) Pabs = 48960 KPa

    b) T = 433.332 °C

    Explanation:

    Pabs = Pgauge + d*g * h

    ∴ d = 1000 Kg/m³

    ∴ g = 9.8 m/s²

    ∴ h = 5000 m

    ∴ P gauge = - 40 KPa * (1000 Pa / KPa) = - 40000 Pa; Pa≡Kg/m*s²

    ⇒ Pabs = - 40000 Kg/ms² + (1000 Kg/m³ * 9.8 m/s² * 5000 m)

    ⇒ Pabs = 48960000 Pa = 48960 KPa

    a) at that height and pressure, we find the temperature at which the water boils by means of an almost-exponential graph which has the following equation:

    P (T) = 0.61094 exp (17.625*T / (T + 243.04)) ... P (KPa) ∧ T (°C) ... from literature

    ∴ P = 48960 KPa

    ⇒ (48960 KPa / 0.61094) = exp (17.625T / (T + 243.04))

    ⇒ 80138.803 = exp (17.625T / (T + 243.04))

    ⇒ Ln (80138.803) = 17.625T / (T + 243.04))

    ⇒ 11.292 * (T + 243.04) = 17.625T

    ⇒ 11.292T + 2744.289 = 17.625T

    ⇒ 2744.289 = 17.625T - 11.292T

    ⇒ 2744.289 = 6.333T

    ⇒ T = 433.332 °C
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