Appendix B: Derivation of Pressure Equation

DOE-STD-3013-2000

APPENDIX B

Derivation of Pressure Equation

B.1.

Introduction

This appendix provides a derivation of the equation used to bound the internal pressure of

storage packages loaded with oxide. It also provides guidance on use of the equation. This

equation appears in DOE-STD-3013-96 [USDOE 1996] and is similar to the equation in DOE-

STD-3013-94 [USDOE 1994b]. For simplicity in comparing the equation derived here with that

used in the 3013 Standard, SI units have not been used. Instead, pressures are given in psi.

It is assumed that the ideal gas law applies to the conditions and gases important to the

calculations. According to that law

PV = nRT

[1]

where P is absolute pressure, V is volume, T is absolute temperature, n is the number of moles

of gas, and R is a constant with units consistent with those chosen for P, V, and T. If a gas is at

some standard condition, described by P0, V0, and T0, then the quantity nR can be evaluated as

n R = P0V0/T0.

[2]

And the pressure under different conditions can be determined by

P1 = nRT1/V1 = P0(V0/V1)(T1/T0).

[3]

In the above equation, T1 is the temperature at which P1 is to be evaluated. V1 is the volume

occupied by the gas at the evaluation temperature.

For ideal gases, the pressure of a mixture of gases can be determined as the sum of the partial

pressures of the individual gases. There are three gas sources that require consideration in a

plutonium storage container: 1) the container fill gas, 2) any gases evolved during storage in

the sealed container through radiolysis, chemical reactions, or desorption, and 3) helium

produced by alpha decay of the contained radioactive species. Thus, the combined effect can

be expressed as:

P = PF + PG + PHe

[4]