Concept explainers
A liquid R-134a bottle has an internal volume of 0.0015 m3. Initially it contains 0.55 kg of R-134a (saturated mixture) at 26°C. A valve is opened and R-134a vapor only (no liquid) is allowed to escape slowly such that temperature remains constant until the mass of R-134a remaining is 0.15 kg. Find the heat transfer with the surroundings that is needed to maintain the temperature and pressure of the R-134a constant.
The heat transfer with the surrounding that is needed to maintain the temperature and pressure of R-134a constant.
Answer to Problem 178RP
The heat transfer with the surrounding that is needed to maintain the temperature and pressure of R-134a constant 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 subscripts 1 and 2 indicates the initial and final states of the system.
Consider the given rigid container as the control volume.
Initially the container is filled with liquid refrigerant and the valve is in closed position, further no other mass is allowed to enter the container. Hence, the inlet mass is neglected i.e.
Rewrite the Equation (I) as follows.
Write the formula for initial specific volume
Write the formula for final specific volume
Here, the volume is
Write the energy balance equation.
Here, the heat transfer is
The process is maintained at isothermal at the open condition of valve, there is no heat transfer while the mass leaves the container .i.e.
The Equation (V) reduced as follows.
At the initial state 1:
The rigid container consist of saturated mixture refrigerant at
Refer Table A-11, “Saturated refrigerant-134a-Temperature table”.
Obtain the following corresponding to the temperature of
The quality of the refrigerant at state 1 is expressed as follows.
The internal energy of the refrigerant at state 1 is expressed as follows.
At the final state (2):
When the valve is opened, the vapor refrigerant only allowed to escape and the temperature is kept constant.
The final temperature of the refrigerant is also
Refer Table A-12, “Saturated refrigerant-134a-Temperature table”.
Obtain the following corresponding to the temperature of
The quality of the refrigerant at state 2 is expressed as follows.
The internal energy of the refrigerant at state 2 is expressed as follows.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Equation (VIII).
Substitute
Substitute
Equation (X).
Here, the temperature is kept constant until the final state and the vapor only exits the tank. Hence the exit enthalpy is expressed as follows.
Refer Table A-12, “Saturated refrigerant-134a-Temperature table”.
The exit enthalpy
Substitute
Thus, the heat transfer with the surrounding that is needed to maintain the temperature and pressure of R-134a constant is
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