Given Information:
- 1 kg of fuel is consumed in 20 days in U-238 nuclear reactor.
- The useful energy per fission is 190 MeV.

To find:
The output power of the reactor.

Formula:
The output power of a nuclear reactor can be calculated using the following formula:

Output Power = (Energy released per fission) × (Number of fissions per unit mass) × (Mass of fuel consumed per unit time)

Solution:

Step 1: Calculate the number of fissions per unit mass
To calculate the number of fissions per unit mass, we need to know the molar mass of U-238 and Avogadro's number.

Molar mass of U-238 = 238 g/mol
Avogadro's number = 6.022 × 10^23 atoms/mol

The number of U-238 atoms in 1 kg of fuel can be calculated as follows:

Number of atoms = (Mass of fuel in grams) / (Molar mass of U-238)
Number of atoms = (1000 g) / (238 g/mol)
Number of atoms = 4201.68 × 10^23 atoms

Since each U-238 atom undergoes fission, the number of fissions per unit mass is equal to the number of atoms in the fuel.

Number of fissions per unit mass = 4201.68 × 10^23 fissions/kg

Step 2: Calculate the mass of fuel consumed per unit time
Mass of fuel consumed per unit time = (Mass of fuel consumed) / (Time)
Mass of fuel consumed per unit time = (1 kg) / (20 days)
Mass of fuel consumed per unit time = 0.05 kg/day

Step 3: Calculate the output power
Output Power = (Energy released per fission) × (Number of fissions per unit mass) × (Mass of fuel consumed per unit time)

Energy released per fission = 190 MeV = 190 × 10^6 eV
1 eV = 1.602 × 10^-19 Joules

Energy released per fission = 190 × 10^6 × 1.602 × 10^-19 J

Output Power = (190 × 10^6 × 1.602 × 10^-19 J) × (4201.68 × 10^23 fissions/kg) × (0.05 kg/day)

Output Power = (190 × 1.602 × 4201.68 × 0.05) × (10^6 × 10^-19 × 10^23) J/day

Output Power = 0.63 × 10^10 J/day

Since the unit of power is Watts, we need to convert the output power from Joules to Watts.

1 Watt = 1 Joule/second
1 day = 24 hours = 24 × 60 × 60 seconds

Output Power = (0.63 × 10^10 J/day) / (24 × 60 × 60 s/day)

Output Power = 730.9028 Watts

Step 4: Convert the output power to megawatts
1 Megawatt = 10^6 Watts

Output Power

C- 45MW