# Homework 6

Answer the following questions. FOR CALCULATIONS SHOW FULL WORK AND FORMULAS.

1) The Ivanpah solar thermal plant being constructed in California (www.ivanpahsolar.com) will use a central tower design with fields of mirrors to reflect incident heat. The goal of the project is to have peak capacity of 392 MW electrical output. Solar radiation is ~1000 W/m2 during peak conditions and the mirrors can reflect 80% of incident solar radiation to the central collector. From there, the heat is used to make steam which is converted to electrical energy with a thermal efficiency of 35%. Calculate the area (in square kilometers) that will need to be covered by mirrors for this project.

2) A typical commercial rooftop solar photovoltaic system produces 5 kW of power during sunlight hours and costs about \$30,000 installed without incentives (or \$15,000 installed with incentives). If you assume 12 hours of sunlight per day (which gives a usage factor of 50%), and assuming you can store electricity for use during nighttime hours, how many homes would need to have rooftop solar systems to power all of Arizona and how much would this cost (with and without incentives) based on the need to supply 7,300 MW of power.

3) A large oak tree produces 2.2 tons of wood over a 50 year growth lifespan. This wood has a heating value of 20 MJ/kg. The tree has a canopy of 10 meters in diameter and it collects solar energy over 6 months each year at an average rate of 177 W/m2. Estimate the tree’s efficiency for converting solar energy to wood heating value. How does this compare to commercial photovoltaic cells today.

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