11454

# 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.

### 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

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.