1. **Problem Statement:** Calculate the thermal energy needed to generate 2143 MWh of electrical energy given 35% efficiency. 2. **Formula:** Energy efficiency formula: $$\text{Efficiency} = \frac{\text{Electrical Energy Output}}{\text{Thermal Energy Input}}$$ 3. **Step 1: Calculate thermal energy needed per day** Given efficiency $\eta = 0.35$ and electrical energy $E_e = 2143$ MWh, $$0.35 = \frac{2143}{E_T} \Rightarrow E_T = \frac{2143}{0.35}$$ 4. **Step 2: Calculate $E_T$** $$E_T = \frac{2143}{0.35} = 6122.857 \text{ MWh}_T$$ 5. **Step 3: Calculate uranium fuel needed** Given 1 kg uranium-235 produces 24000 MWh$_T$, Fuel needed per day: $$\text{Fuel}_{day} = \frac{6122.857}{24000} = 0.2551 \text{ kg}$$ 6. **Step 4: Calculate fuel for longer periods** - 1 month (30 days): $$0.2551 \times 30 = 7.653 \text{ kg}$$ - 1 year (365 days): $$0.2551 \times 365 = 93.07 \text{ kg}$$ - 50 years: $$93.07 \times 50 = 4653.5 \text{ kg}$$ 7. **Step 5: Calculate cost of fuel per day** Cost per kg uranium = 88, $$\text{Cost}_{fuel} = 0.2551 \times 88 = 22.45$$ 8. **Step 6: Calculate operating cost per day** Operating cost = 33 per MWh electrical, $$33 \times 2143 = 70719$$ 9. **Step 7: Total daily cost** $$22.45 + 70719 = 70741.45$$ **Final answers:** - Thermal energy needed per day: $6122.86$ MWh$_T$ - Uranium fuel needed: day $0.2551$ kg, month $7.653$ kg, year $93.07$ kg, 50 years $4653.5$ kg - Daily fuel cost: $22.45$ - Daily operating cost: $70719$ - Total daily cost: $70741.45$