Concept explainers
The final temperature and mass of the air in the ballast tank.

Answer to Problem 176RP
The final temperature and mass of the air in the ballast tank is
Explanation of Solution
Write the general mass balance equation.
Here, the inlet mass flow rate is
It is given that the mass of air pumped into the tank to get the submarine to the surface. Here, there is no exit mass of air. Thus, the exit mass
Refer Equation (I).
Write the mass balance equation for air.
Here, the subscript
While air entering into the ballast tank, the seawater present in the tank is released to the sea. Here, there is no inlet mass of water. Thus, the inlet mass
Refer Equation (I).
Write the mass balance equation for water.
Here, the subscript
Write the general energy rate balance equation.
Here, the rate of total energy in is
The system is at steady state. Hence, the rate of change in net energy of the system becomes zero.
Refer Equation (IV).
Write the energy balance equation for the system (ballast tank).
Here, the mass is
Substitute
Integrate the Equation (VI) at initial (1) and final (2) states.
The enthalpy and internal energy is expressed as follows.
The mass of air is expressed as follows.
Here, the specific volume is
For water the specific heat is
At final state, the mass sea water is zero and the ballast is completely filled with air.
Rewrite the Equation (VII) as follows.
Here,
The specific heat ratio is,
The initial and final pressure of air is,
Rewrite the Equation (VIII) as follows.
Write the formula for mass flow rate of air at final state.
Refer Table A-1, “Molar mass, gas constant, and critical-point properties”.
The gas constant
Refer Table A-2a, “Ideal-gas specific heats of various common gases”.
The specific heat ratio
Conclusion:
Substitute
Substitute
Thus, the final temperature and mass of the air in the ballast tank is
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