January 9, 2015

Fig. 1: House Layout. |

With climate change on the horizon, the United States of America is one of the leading contributors of harmful greenhouse gases. Despite the knowledge of the existence of global warming, many American households have yet to take advantage of all of the energy-conserving measures available to them. The difference is particularly striking in comparison with the lifestyle habits embraced by their Westernized European counterparts. This paper seeks to quantify the amount of energy that could be conserved by an average American home, if more European habits were to be adopted. In particular, a comparison will be struck between a middle-class American family home and a comparable middle-class German home, as perceived by the author's personal observations.

For the sake of an equitable comparison, this analysis will take place on a home of comparable size and comparable occupancy. In this scenario, it will be assumed that two adults and two children live in a home with three bedrooms, two bathrooms, a kitchen, a dining room, and a recreational room. A layout is shown in Fig. 1, where the ceiling height is assumed to be 3 meters. The scene will be set on a day with an outside air temperature of 50 degrees Fahrenheit. This temperature would be a reasonable approximation of an autumn or spring day, either in Germany or in the upper latitudes of the United States.

There are three main notable household differences: showering habits, kitchen appliance usage, and house heating strategies. As a disclaimer, all habits are based on the author's observation of a select few personal homes. This analysis is not intended to be an exact representation of standard behavior for an entire country, but merely showcase the benefits that could potentially be gained by an adaptation of alternative ways, and simplifying assumptions will be made where necessary.

It has been said that Germans are known for their
efficiency, and the bathroom is no exception. In an effort to conserve
water, one can frequently expect to hear the water being turned on and
off multiple times throughout the course of a German shower. Instead of
turning the water on and luxuriating in the flow for the duration of a
shower, it is common to quickly rinse, turn the water off, apply shampoo
and soap, and only then turn the water on once more to rinse away the
lather. An American shower, on the other hand, is 8 minutes on average,
with no such interruption in the middle. [1] Assuming a water flow rate
of 2.5 gallons per minute, an 8 minute shower, a ground water
temperature of 50 degrees Fahrenheit, and a shower temperature of 100
degrees Fahrenheit, this means that an American household of four
expends 80 gallons of water, and 35.3 megajoules (MJ) of energy in
bathing every day (assuming that those 80 gallons are heated
instantaneously with no losses, E = C_{p} V ΔT, where
C_{p} is specific heat capacity, V is volume, and ΔT is
the change in water temperature). By shutting the water off during
lathering, water usage times could be cut in half, thereby conserving 40
gallons of water and 17.6 MJ of energy.

Everything is more compact in a German kitchen, the refrigerator included. American culture has made it easy, and indeed preferable, to save money on groceries by buying items in bulk, and stocking up on groceries once every week or two. In Germany, however, it is more common to go to the grocery store once every few days. Food is fresher, more locally sourced, and contains fewer preservatives. As such, their refrigerators are much smaller, and therefore consume less energy by cooling a smaller volume. In fact, specifications for common refrigerator styles show a great disparity between the two types: the Bomann KS 163.1 consumes 1.71 MJ per day (Germany), whereas the LG Refrigerator Model LFC24770ST consumes 4.65 MJ per day (America), a savings of a factor of nearly 3. [2,3]

The final notable household difference is the most difficult to implement after a house is constructed, but potentially the largest energy saver. The majority of German houses have well partitioned rooms, all separated by solid walls and doors. Each room is heated separately, and only when in use. Here, we calculate a rough approximation of the energy used to heat a house over the course of a day, neglecting heater efficiencies, and assuming a constant outside air temperature. Any increase in indoor temperature is approximated as an instantaneous addition of energy, with no outside energy losses.

where E is energy, C_{p} is the specific heat
capacity of air, and &*delta;T is the temperature increase. Over time,
heat will seep out of a room. We approximate this seepage as conduction
out of the room through any external walls, neglecting internal house
walls. The walls are assumed to be 15 cm thick and made out of bricks.
Brick is assumed to have a thermal conductivity of 0.15 W/m/K. [4]
Seepage is calculated over 2 second increments over the course of the
whole time frame, using the following two equations:

E | = | k A (T_{inside} - T_{outside}) t / d |

ΔT | = | E / (C_{p} V) |

where E is the energy loss through the wall, k is the
wall conductivity, A is the wall area, T is a temperature (either inside
or outside as indicated), d is the wall thickness, t is the time
duration, ΔT is the temperature change due to heat loss,
C_{p} is the specific heat capacity, and V is the room
volume.

Assume that the whole house is at 65 degrees. Heating the whole house to 75 degrees requires 1.77 MJ of energy.

The house stays at 75 degrees for two hours while the family prepares for the day. Maintaining this temperature requires 11.4 MJ of energy.

The family leaves, and the house drops to 65 degrees for the next nine hours. It starts at 75 degrees, and reaches 65 degrees after 18 minutes. Maintaining 65 degrees then requires 29.7 MJ of energy.

The family arrives home, and the house heats up to 75 degrees again, requiring 1.77 MJ of energy. Maintaining this temperature for two hours requires 28.5 MJ.

The family goes to sleep, the house cools down to 65 degrees after 18 minutes, and maintaining 65 degrees requires 26.3 MJ of energy, until they wake up the next morning and the cycle begins again.

Assume that the bedrooms are at 65 degrees. The rest of the house is at 50 degrees (ambient temperature). Heating the bedrooms, kitchen, and bathroom to 75 degrees takes 1.11 MJ of energy.

The kitchen stays warm for half an hour: 0.6 MJ

The bathroom and bedrooms stay warm for two hours: 6 MJ

The family leaves, and the house cools down for nine hours. All rooms cool down to 50 degrees.

The family returns, and heats the bedrooms, kitchen, and living room up. This requires 2.77 MJ.

The bedrooms and living room stay at 75 for 5 hours: 19.5 MJ

The kitchen stays at 75 for an hour and a half: 1.8 MJ

The family goes to bed, the living room heat turns off, and the bedrooms cool down to 65 degrees. The bedrooms take 15 minutes to cool down, and 11.2 MJ are expended to maintain the temperature until the next morning and the cycle begins again.

Tallying up all of these calculations, we see that a typical German home uses roughly 42.9 MJ to heat their home on a cool day, whereas a typical American home uses roughly 99.4 MJ. This is over a factor of two savings.

Not only is a German household more energy efficient, saving on resources consumed, a fair amount of homes have additional measures in place to save on energy price. Some are equipped with water and room heating systems that charge overnight, and then use up that stored energy over the day. Since energy prices are generally lower overnight, this is an effective cost saving strategy.

In this paper, we have shown that if a typical American household were to adopt some of the energy-conserving habits of a typical German household, their energy usage could be reduced by over a factor of two. The analysis was done assuming lossless heating, however, if an American home were to be heated by a similarly efficient method as a German home, then the savings would still be roughly a factor of two. In colder regions and at cooler times of the year, the savings could be even greater. Not only does this reduce the electricity bills every month, but with climate change on the horizon, every effort should be taken when it comes to conserving our planet.

© Ashley Clark. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

[1] M. Morin, "Americans Use Twice as Much Water as They Think They Do, Study Says," Los Angeles Times, 3 Mar 13.

[2] "Bohmann Appliances 2014/2015," C. Bohmann GmbH, August 2014, p. 23.

[3] "Energy Guide for LG Refrigerator Models," LG Electronics, 29 Aug 13.

[4] F. W. Sears, M. W. Zemansky, and H. D. Young,
*University Physics, 7th Ed.* (Addison Wesley, 1987), Table
15-5.