# Guy-Lussac’s Law

Guy-Lussac’s law or the pressure law is one of the gas laws, and it states that:

For a fixed mass of gas at constant volume, the pressure is directly proportional to the Kelvin temperature.

Guy-Lussac’s Law or the Pressure Law is one of the gas laws. In the late 18th and early 19th centuries, it was discovered by French chemist Joseph Louis Gay-Lussac. He studied the relationship between the pressure and the temperature of a gas at constant volume. The results of certain experiments with gases at relatively low pressure led Joseph Louis Gay-Lussac to formulate a well-known “Pressure Law”. It states that:

For a fixed mass of gas at constant volume, the pressure is directly proportional to the Kelvin temperature.

That means that, for example, if you double the temperature, you will double the pressure. If you halve the temperature, you will halve the pressure.

You can express this mathematically as:

p = constant . T

Yes, it seems to be identical to the isochoric process of an ideal gas. These results are fully consistent with the ideal gas law, which determinates that the constant is equal to nR/V. If you rearrange the pV = nRT equation by dividing both sides by V, you will obtain:

p = nR/V  .  T

where nR/V is constant and:

• p is the absolute pressure of the gas
• n is the amount of substance
• T is the absolute temperature
• V is the volume
• R  is the ideal, or universal, gas constant, equal to the product of the Boltzmann constant and the Avogadro constant,

In this equation, the symbol R is the universal gas constant that has the same value for all gases—namely, R =  8.31 J/mol K.

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:

Gas Laws

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