Energy Balance on Pressurizing a Tank

A gas flows through a pipe into an insulated tank (0.1 ) that is initially at a lower pressure and at a different temperature. Click the “valve (open)" play button to start gas flow into the tank; the valve closes when the pressures equalize. The tank initially contains either an ideal gas () and more is added, or it contains a vapor-liquid mixture of water and superheated steam is added. Sliders change the pipe pressure and temperature and the initial tank pressure. The initial mass of water in the tank is 1 kg and that does not change when the initial tank pressure is changed with the slider. Initially the tank is at the saturation temperature of water at the initial pressure. Use the "valve (reset)” button to go back to the initial conditions before the valve was opened.

SNAPSHOTS

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DETAILS

Energy Balance
,
where the subscript refers to what is initially inside the tank, refers to what is added or in the line, is mass (kg), is the internal energy (kJ/kg), and is enthalpy (kJ/kg).
For a Non-Ideal System, Using Water
.
Since two phases are present in the tank at all times, the quality of the steam needs to be calculated:
,
,
,
where the superscripts and refer to the specific liquid and vapor properties (per kg), is the volume of the tank (), is the mass of steam added to the tank from the line, and is the enthalpy at the line temperature and pressure . The value is unknown; it has to be solved for in order to evaluate the conditions of the system.
,
.
Now these expressions can be substituted into the energy balance (remember ) and solved for .
Since two phases are present in the tank, the final temperature of the system is the saturation temperature at the final pressure .
For an Ideal Gas System
The number of moles initially in the tank can be calculated using the ideal gas law:
.
The internal energy and enthalpy are found by defining a reference point .
At , ,
,
,
.
The number of moles in the tank at equilibrium can also be calculated using the ideal gas law:
.
This equation can be substituted into the energy balance to solve for the final temperature .
.
The subscript refers to the gas in the tank before more gas is added, the subscript refers to the gas in the line, the subscript denotes a reference state, is pressure (bar), is volume (L), is the ideal gas constant ([L bar]/[mol K]), is temperature (°C), is internal energy (J/mol), is the constant-volume heat capacity for an ideal gas (J/[mol K]), and is enthalpy (J/mol).
The screencast video at [1] explains how to use this Demonstration.
Reference
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