Homework #4 Nuclear and Solar Energy
Question 1
Carry out the rudimentary design of a small modular nuclear reactor that delivers 100 MWe. The reactor is based on a Rankine cycle where the steam is expanded in a turbine from 12.5 MPa and 350°C to condensed water at 5 kPa.Assume that the generator is 98% efficient, the actual cycle achieves 90% of the efficiency of the ideal cycle, and 90% of the thermal energy released in the nuclear reactions is transferred to the working fluid. If the reactor uses uranium as a fuel which is enriched to 3% U-235, what mass of fuel is consumed each year? Provide your answer in kg/year.
Question 2
What is the flow rate of steam in kg/s required when the reactor in problem 1 is running at full power? Provide your answer in kg/s.
Question 3
Suppose in Problem 1 that the reactor has a capital cost of $1500/kWe costs $5 million per year for refueling, and $6 million per year for nonfuel maintenance costs. If the project lifetime is 25 years and MARR=6%, what is the levelized cost of electricity per kWh? Provide your answer in $/kWh.
Question 4
A reactor has a rated capacity of 1 GWe and produces 7.9 billion kWh/year. It is fueled using fuel rods that contain 2.5% U-235 by mass. The electric generator is 98% efficient, the thermal cycle of the plant is 33% efficient and 90% of the thermal energy released in fission is transferred to the working fluid. What is the capacity factor of the plant? (The capacity factor is the actual output divided by hypothetical output if the plant had operated at maximum capacity for the entire year). Provide your answer as a percentage (ex. If your answer is 0.123, enter '12.3').
Question 5
For the reactor in Problem 4, What is the rate of U-235 consumption in milligrams/second in order to deliver the average output?
Question 6
For the reactor in Problem 4, what is the total mass of fuel rods consumed each year? Provide your answer in kg/year.
Question 7
For the reactor of Problem 4 and based on the amount of energy released in fission reactions, what is the reduction in mass of fuel each year? Provide your answer in kg/year.
Question 8
Consider a photovoltaic cell, which achieves a 97% collection efficiency for photons in the range of energy values from 1.5 × 10-19 J to 6.00 × 10-19 The absorption coefficient is 82%. Photons arrive at the surface of the panel at a rate of. Photon energy values have a Weibull distribution with measured in units of. Using the Weibull probability distribution for frequency of photons as a function of energy, calculate / for this device. Provide your answer in A/m2.
Weibull probability density function:
Question 9
Given a PV cell with light current 0.035 A/cm2 and saturation current 1.5 x 10-10 A/cm2, calculate maximum voltage if the ambient temperature is 32°C. Use parameter m=1. Provide your answer in mV. (Ex., if your answer is 0.1234 V, enter '123.4').
Question 10
Given a PV cell with light current 0.035 A/cm2 and saturation current 1.5 x 10-10 A/cm2, calculate maximum current if the ambient temperature is 32C. Use parameter m = 1. Provide your answer in mA/cm2.
Question 11
1. Given a PV cell with light current 0.035 A/cm2 and saturation current 1.5x 10-10 A/cm2, calculate fill factor if the ambient temperature is 32°C. Use parameter m = 1. Provide your answer as a percentage. (Ex, if your answer is 0.123, enter '12.3').