Example of Ideal Gas Law – Gas Compression

Example: Ideal Gas Law – Gas compression inside a pressurizer

pressurizer
A pressurizer is a key component of PWRs.

Pressure in the primary circuit of PWRs is maintained by a pressurizer, a separate vessel that is connected to the primary circuit (hot leg) and partially filled with water which is heated to the saturation temperature (boiling point) for the desired pressure by submerged electrical heaters. During the plant heatup the pressurizer can be filled by nitrogen instead of saturated steam.

Assume that a pressurizer contains 12 m3 of nitrogen at 20°C and 15 bar. The temperature is raised to 35°C, and the volume is reduced to 8.5 m3. What is the final pressure of the gas inside the pressurizer? Assume that the gas is ideal.

Solution:

Since the gas is ideal,we can use the ideal gas law to relate its parameters, both in the initial state i and in the final state f. Therefore:

pinitVinit = nRTinit

and

pfinalVfinal = nRTfinal

Dividing the second equation by the first equation and solving for pf we obtain:

pfinal = pinitTfinalVinit / TinitVfinal

Note that we cannot convert units of volume and pressure to basic SI units, because they cancel out each other. On the other hand we have to use Kelvins instead of degrees of Celsius. Therefore Tinit = 293 K and Tfinal = 308 K.

It follows, the resulting pressure in the final state will be:

pfinal = (15 bar) x (308 K) x (12 m3) / (293 K) x (8.5 m3) = 22 bar

 
References:
Reactor Physics and Thermal Hydraulics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.

See above:

Ideal Gas Law