# Problem Set 1

## Problem 1

It is important to have a general idea of how much energy can be stored and extracted from a certain form of storage. Record the specific energies of the listed storage types. Then make a chart (generated in Matlab, Excel, or similar) to display the relative specific energies.

Extra credit: Plot the specific energies vs. the cost/Joule of each storage type.

Storage Type Specific energy (MJ/kg)

Alkaline battery
Capacitor
Coal
Flywheel
Gasoline
Hydrogen
Lithium ion battery
Super capacitor
A storage method of interest to you

## Problem 2

In this problem you will be using estimation to measure how much energy goes into heating water for showers in MA. Remember to state your assumptions clearly – you’ll find that an estimate may be completely off because of just one assumption (but, conveniently, it’s common that two bad assumptions can cancel each other out). Further, explicitly stating assumptions is key to the design process. We will start you off with the following assumption:

Assumption: Hot water for showering is about 105° F

1. How much hot water is used in a single hot shower?
2. How much hot water is used in showers throughout MA. Keep in mind that some people do not take hot showers.
3. How much energy is needed to heat water for showers throughout MA? Remember that heating water is not a 100% efficient process.
4. Suppose you designed a shower head that halved the volumetric flow of water coming out from the shower without any negative impacts on showering. How much money could you save all the residents of MA? How much would you price the product at?
5. Inspired by this problem set, you decide to build your own solar water heater with an efficiency of 25%. How large a solar water heater would you have to build so that the average family would have hot showering water? What about all of the residents of MA? You can neglect heat losses in storage/transport.

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