An adiabatic 0.2-m3 storage tank that is initially evacuated is connected to a supply line that carries nitrogen at 225 K and 10 MPa. A valve is opened, and nitrogen flows into the tank from the supply line. The valve is closed when the pressure in the tank reaches 10 MPa. Determine the final temperature in the tank (a) treating nitrogen as an ideal gas, and (b) using generalized charts. Compare your results to the actual value of 293 K.
FIGURE P12–101
(a)
The final temperature in the tank by treating nitrogen as an ideal gas and compare the result to the actual value of
Answer to Problem 101RP
The final temperature in the tank by treating nitrogen as an ideal gas is
Explanation of Solution
Write the equation of mass balance.
Here, the inlet mass is
The change in mass of the system for the control volume is expressed as,
Here, the suffixes 1 and 2 indicates the initial and final states of the system.
Consider the given insulated tank as the control volume.
The valve is closed when the pressure in tank reaches to
Rewrite the Equation (I) as follows.
Write the energy balance equation.
Here, the heat transfer is
Since the tank is adiabatic, there is no heat transfer i.e.
The Equation (III) reduced as follows.
Substitute
Express the Equation (V) in molar basis.
Here, the molar mass of nitrogen is
Conclusion:
The inlet condition of the nitrogen is
While considering the nitrogen as the ideal gas, its enthalpy is solely depends on temperature.
Refer Table A-18, “Ideal-gas properties of nitrogen,
The molar enthalpy of nitrogen corresponding to the temperature of
Refer Equation (VI).
The final temperature of the nitrogen is expressed as follows.
Refer Table A-18, “Ideal-gas properties of nitrogen,
The final temperature
Thus, the final temperature in the tank by treating nitrogen as an ideal gas is
The percentage error with the actual temperature value of
The error associated is
(b)
The final temperature in the tank by using generalized departure charts.
Answer to Problem 101RP
The final temperature in the tank by using generalized departure charts is
Explanation of Solution
Refer Table A-1, “Molar mass, gas constant, and critical-point properties”.
The critical temperature and pressure of nitrogen gas is as follows.
The reduced pressure
At inlet:
Refer Figure A-29, “Generalized enthalpy departure chart”.
The enthalpy departure factor
Write formula for enthalpy departure factor
Here, the inlet molar enthalpy at ideal gas state is
Rearrange the Equation (I) to obtain
Write the formula for molar enthalpy at final state
Write the formula for molar internal energy at final state.
Here, the compressibility factor is
The universal gas constant
Conclusion:
Refer part (a) answer for
Substitute
Refer Equation (VI).
It is given that the actual final temperature of nitrogen is
Consider the exit temperature
The reduced pressure
Refer Figure A-29, “Generalized enthalpy departure chart”.
The enthalpy departure factor
Refer Figure A-15, “Nelson–Obert generalized compressibility chart”.
The compressibility factor
Refer Table A-18, “Ideal-gas properties of nitrogen,
The final molar enthalpy of nitrogen
Substitute
Substitute
Consider the exit temperature
The reduced pressure
Refer Figure A-29, “Generalized enthalpy departure chart”.
The enthalpy departure factor
Refer Figure A-15, “Nelson–Obert generalized compressibility chart”.
The compressibility factor
Refer Table A-18, “Ideal-gas properties of nitrogen,
The final molar enthalpy of nitrogen
Substitute
Substitute
Express interpolation formula to determine the final temperature
Substitute
Thus, the final temperature in the tank by using generalized departure charts is
The percentage error with the actual temperature value of
The error associated is
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Chapter 12 Solutions
Thermodynamics: An Engineering Approach
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