
The final mass of the air in the ballast tank and total heat transfer.

Answer to Problem 174RP
The final mass of air in the ballast tank is
The total heat transfer is
Explanation of Solution
Write the formula for mass of air
Here, the volume of air is
Write the formula for mass of water at initial.
Write the general energy balance equation.
Here, the total energy in is
Refer Equation (IV).
Write the energy balance equation for the system (ballast tank).
Here, the mass is
At final state 2:
The mass of water in the tank is zero. Only air is present in the ballast tank. Hence, the final state energy of the tank is expressed as follows.
At initial state 1:
Both air and water is present in the tank. The initial state energy of the tank is expressed as follows.
The inlet mass of air is expressed as,
Here, the inlet mass is mass of air and the exit mass is mass of water.
Rewrite the Equation (V) as follows.
Refer Table A-4, “Saturated water-Temperature table”.
The enthalpy
It is given that the pressure and temperature of air is kept constant.
The Equation (VI) is reduced as follows.
The specific volume
Refer Table A-1, “Molar mass, gas constant, and critical-point properties”.
The gas constant
Refer Table A-2, “Ideal-gas specific heats of various common gases”.
The specific heat at constant pressure
The specific heat at constant volume
Conclusion:
Here,
Substitute
Substitute
Thus, the final mass of air in the ballast tank is
Substitute
Substitute
Here, the negative sign indicates that the heat is removed.
Thus, the total heat transfer is
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