Concept explainers
An insulated 0.15-m3 tank contains helium at 3 MPa and 130°C. A valve is now opened, allowing some helium to escape. The valve is closed when one-half of the initial mass has escaped. Determine the final temperature and pressure in the tank.
The final temperature and pressure in the tank.
Answer to Problem 128P
The final temperature in the tank is
The final pressure in the tank 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 tank as the control volume. Initially the tank is filled with helium and the valve is closed. No mass is allowed to inlet the tank i.e.
Rewrite the Equation (I) as follows.
It is given that the valve is opened until the initial mass of the helium reached into half (final mass).
Write the formula for initial and final masses.
Here, the pressure is
Write the energy balance equation.
Here, the heat transfer is
When the valve is opened the mass (helium) is allowed to escape and no work is done i.e.
The Equation (VI) reduced as follows.
Write the general expressions for enthalpy and internal energy.
Here, the specific heat at constant pressure is
Here, the enthalpy of the helium changes continuously while leaving the tank. For simplicity, consider the properties of exiting helium as constant corresponding to the average temperature of initial and final states.
Rewrite the equation (VII) as follows with reference to the exit enthalpy and general expression of internal energy.
Refer Table A-2 (a), “Ideal-gas specific heats of various common gases”.
The specific heat at constant pressure
Conclusion:
Substitute
Substitute
Divide the Equation (IX) by
Divide the Equation (X) by
The specific heat ratio is,
Substitute
Substitute
Thus, the final temperature in the tank is
Divide the Equation (V) by Equation (IV).
Here, the volume of the tank cannot change. Hence, the initial and final volumes are equal.
The Equation (XII) becomes as follows.
Substitute
Thus, the final pressure in the tank is
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Chapter 5 Solutions
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