Appendix B. Derivation of Pressure Equation

DOE-STD-3028-2000

Appendix B. Derivation of Pressure Equation

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

storage package. It also provides guidance on use of the equation. It is assumed that the Ideal

Gas Law applies to the conditions and gases important to the calculations. According to that

law

PV = nRT

(B.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

(P0 )(V0 )

nR =

(B.2)

At constant volume the pressure under different temperature conditions can be determined by

T 

T1 = P0  1 

P1 =

(B.3)

T 

 0

In the above equation, T1 is the temperature at which P1 is to be evaluated. In the case of a

storage can, the volume, V, will simply be the interior volume of the outer container, less the

volume occupied by internal containers, less the volume occupied by the 233U oxide material.

This volume can be calculated as

V = Vc -

(B.4)

where Vc is the volume of the container, m is the mass of the oxide and ρ is the density of the

oxide. Densities for uranium oxides are given in Table B.1. For cases where the stoichiometry

is not known, the most limiting density (7300 kg/m3 or 456 lbm/ft3) should be used.