Question 5.12: According to Table 5.8, U-233, U-235, U-238, and Pu-249 are ......
According to Table 5.8, U-233, U-235, U-238, and Pu-249 are all non-1/v absorbers. If their absorption cross sections at 0.025 eV are 574.25 barns, 681.77, 2.717, and 1017.40 barns, what values should we use for their absorption cross sections for the entire thermal energy range? Assume the operating temperature of the fuel is 1000°C. S
| TABLE 5.8 | ||||||||||
| Non-1/v Factors G(T) for Some Common Nuclear Materials | ||||||||||
| T (°C) | Cd | Sm-149 | X-135 | \frac{U-233}{G_f} | \frac{U-233}{G_a} | \frac{U-235}{G_f} | \frac{U-235}{G_a} | \frac{U-238}{G_a} | \frac{Pu-239}{G_f} | \frac{Pu-239}{G_a} |
| 30 | 1.32 | 1.62 | 1.16 | 0.99 | 1.00 | 0.98 | 0.89 | 1.00 | 1.05 | 1.07 |
| 100 | 1.60 | 1.89 | 1.21 | 0.99 | 1.00 | 0.96 | 0.96 | 1.00 | 1.11 | 1.16 |
| 200 | 1.96 | 2.09 | 1.23 | 0.99 | 1.00 | 0.94 | 0.95 | 1.00 | 1.25 | 1.34 |
| 400 | 2.56 | 2.18 | 1.19 | 1.00 | 1.00 | 0.92 | 0.93 | 1.00 | 1.69 | 1.89 |
| 600 | 2.90 | 2.08 | 1.09 | 1.00 | 1.01 | 0.91 | 0.92 | 1.01 | 2.20 | 2.53 |
| 800 | 3.05 | 1.92 | 0.99 | 1.01 | 1.02 | 0.90 | 0.92 | 1.02 | 2.66 | 3.10 |
| 1000 | 3.06 | 1.76 | 0.89 | 1.02 | 1.03 | 0.89 | 0.91 | 1.02 | 3.00 | 3.54 |
| Source: Lamarsh, J.R. and Baratta, A.J., Introduction to Nuclear Engineering, Prentice Hall, Upper Saddle River, NJ, 2001. | ||||||||||
Their absorption cross sections for the entire thermal energy range can be found from the equation σ_a = G × σ_a (0.025 eV), where G is the non-1/v factor shown in Table 5.8. Since the values of G for U-233, U-235, U-238, and Pu-239 are 1.02, 0.91, 1.02, and 3.54, respectively when the flux is Maxwellian and the operating temperature of the fuel is 1000°C, the absorption cross sections we should use are σ_{a233} = 1.02 × 574.25 = 585.74 barns, σ_{a235} = 0.91 × 681.77 = 630.40 barns, σ_{a238} = 1.02 × 2.717 = 2.771 barns, and σ_{a239} = 3.54 × 1017.40 = 3601.60 barns. Notice that each of these cross sections can be interpreted as the thermal group cross sections in this case because the thermal energy range is defined to exist between 0 and 1 eV.