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A rigid, sealed tank initially contains 2000 kg of water at 30 °C and atmospheric pressure. Determine: a) the volume of the tank (m3 ). Later, a pump is used to extract 100 kg of water from the tank. The water remaining in the tank eventually reaches thermal equilibrium with the surroundings at 30 °C). Determine: b) the final pressure (kPa).

User Prelic
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Given:

mass of water, m = 2000 kg

temperature, T =
30^(\circ)C = 303 K

extacted mass of water = 100 kg

Atmospheric pressure, P = 101.325 kPa

Solution:

a) Using Ideal gas equation:

PV = m
\bar{R}T (1)

where,

V = volume

m = mass of water

P = atmospheric pressure


\bar{R} = (R)/(M)

R= Rydberg's constant = 8.314 KJ/K

M = molar mass of water = 18 g/ mol

Now, using eqn (1):


V = \frac{m\bar{R}T}{P}


V = (2000* (8.314)/(18)* 303)/(101.325)


V = 2762.44 m^(3)

Therefore, the volume of the tank is
V = 2762.44 m^(3)

b) After extracting 100 kg of water, amount of water left, m' = m - 100

m' = 2000 - 100 = 1900 kg

The remaining water reaches thermal equilibrium with surrounding temperature at T' =
30^(\circ)C = 303 K

At equilibrium, volume remain same

So,

P'V = m'
\bar{R}T'


P' = (1900* (8.314)/(18)* 303)/(2762.44)

Therefore, the final pressure is P' = 96.258 kPa

User Nevf
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