Concept explainers
An insulated tank that contains 1 kg of O2 at 15°C and 300 kPa is connected to a 2-m3 uninsulated tank that contains N2 at 50°C and 500 kPa. The valve connecting the two tanks is opened, and the two gases form a homogeneous mixture at 25°C. Determine (a) the final pressure in the tank, (b) the heat transfer, and (c) the entropy generated during this process. Assume T0 = 25°C.
FIGURE P13–56
(a)
The pressure of the mixture.
Answer to Problem 56P
The pressure of the mixture is
Explanation of Solution
Refer to Table A-2, obtain the constant-volume specific heats of the gases at room temperature.
Write the equation to calculate the volume of the oxygen tank.
Here, mass of oxygen tank is
Calculate the mass of nitrogen gas.
Here, initial temperature and pressure of nitrogen gas is
Calculate the total volume.
Calculate the mole numbers of
Here, molar mass of
Calculate the mole number of the mixture.
Calculate the pressure of the mixture.
Here, universal gas constant of the mixture is
Conclusion:
Refer to Table A-1, obtain the gas constants of
Substitute 1 kg for
Substitute
Substitute
Refer to Table A-1, obtain the molar mass of
Substitute 1 kg for
Substitute 10.43 kg for
Substitute
Substitute
Thus, the pressure of the mixture is
(b)
The heat transfer.
Answer to Problem 56P
The heat transfer is
Explanation of Solution
Write the equation of energy balance for a closed system.
Here, heat output is
Conclusion:
Substitute 1 kg for
Thus, the heat transfer is
(c)
The entropy generation.
Answer to Problem 56P
The entropy generation is
Explanation of Solution
Write the equation of entropy balance.
Here, entropy at inlet and exit is
Calculate the mole fraction of
Calculate the value of
Here, the partial pressure of mixture at state 2 is
Calculate the value of
Here, the partial pressure of mixture at state 2 is
Conclusion:
Substitute
Substitute
Refer to Table A-2, obtain the constant-pressure specific heats of the gases at room temperature.
Substitute 0.077 for
Substitute 0.923 for
Substitute
Thus, the entropy generation is
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Chapter 13 Solutions
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