# Should You Get a Tesla Home Battery? Let Physics Explain

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Categories: Energy

Tesla announced a battery for your house, the Powerwall. I think this is a great opportunity to talk about batteries and physics. Let me answer some questions you might have.

**Why would you want a battery for your house?**

This is perhaps the most important question and one that has likely been addressed many times. In short, a house battery will let you be more power independent. If you have solar panels or electricity generated from wind, they don’t always produce the same amount of power. With a battery, you can store this energy during the day (or during wind) and then use it at night.

A house battery will also let you get power from the electric company at night when the rates are lower and then use it during the day. Really, that’s win-win. You win with a lower power bill and the electric company wins with lower demand during the day.

**How is the Powerwall different than other batteries?**

You could always have a battery for your house. The most common way was to use lead acid batteries, like the one in your car. However, this was not so simple. You would need to have a whole bunch of the batteries and you would have to connect them together. When one battery goes out, you have to replace it. Oh, the traditional battery is also expensive and takes up lots of space.

The Powerwall seems to make a home battery more like an appliance. It mounts on the wall and you don’t have to maintain individual batteries, and the price seems reasonable at between $3,000 to $3,500.

**So, you could just get this battery and run your house?**

Actually, no. Your house runs on AC current but the battery gives you DC current. This means that you need to take the DC current and convert it to AC current. You might have a device that does this in your car so that you can plug in household items like a computer or a coffee pot. The converter takes the DC current from the car battery and turns it into an AC current so that your laptop can then take this AC current and convert it back to DC. Yes, that seems silly but it’s true. The Powerwall does not include a DC to AC converter (or AC to DC if you want to charge from the power grid).

**How long could you run your house with a Powerwall?**

Tesla makes a 7 and 10 kilowatt-hour battery. Let’s look at the 10 kWh one—but Tesla says that you can stack these such that you could make a 20 kWh battery if that made you happy. But really, this comes down to the definition of power as the rate that you do work (or change energy).

We know the energy stored in the battery and we can estimate the average power the house uses. From that, I can solve for the time to use this energy stored in the battery.

What is the energy stored in a battery? The bigger Powerwall has 10 kWh. Yes, this is a unit of energy and not power. It says that you could get a power of 10 kilowatts for 1 hour. You can convert this energy to Joules if you like – it would be 3.6 x 10^{7} Joules (1 watt is a Joule/second).

The next thing we need to calculate the run time is the power. How much power does your house use? I think 2 kilowatts is a good estimate. With that, we can calculate the time:

Five hours doesn’t seem like a long time, but I bet this would get you through the night if you are using solar power (you don’t use as much energy when you are asleep). Ok, actually you would get less than 5 hours. This calculation assumes everything is 100% efficient. In fact, the battery is only 92 percent efficient and the DC to AC converter would have some energy loss as well. If you aimed for 3 hours at 2 kW, I think you would be ok.

**What is energy density?**

If I talk about density, you will probably think of the mass of an object divided by its volume. This would be the mass-density. Energy density is the energy stored in a device divided by its volume. Simple, right? But why would you need this? Well, it tells you how large a storage device will need to be to store a certain amount of energy.

What is the energy density for the Powerwall? From the Powerwall page, the battery has dimensions of 130 cm x 86 cm x 18 cm. Assuming this is a perfect rectangular cube it would have a volume of 0.201 m^{3}. With 3.6 x 10^{7} Joules (or 36 MJ) of stored energy, the Powerwall has an energy density of 179 MJ/m^{3} or 0.179 MJ/L – I don’t know why people like energy densities in Joules per liter.

How does this energy density compare to other things? This Wikipedia page lists the energy density of various mediums. Looking at this data, the energy density for the Powerwall seems rather low since a lead-acid battery has a density of 0.56 MJ/L. However, maybe this is due to extra space in the Tesla battery. There is also a mass energy density (energy per unit mass). The Powerwall has a mass of 100 kg which puts the mass energy density at 0.36 MJ/kg. This value puts the Powerwall right in the rand for Lithium-ion batteries.

**Can you assign some physics homework for the Powerwall?**

Of course. Homework is my favorite part. Here are some questions for you to consider.

- How long could you run your smart phone using the Powerwall as your battery? Here is some help on phone batteries.
- What if you put this Powerwall in your Tesla car? What kind of range would you get? How does this Powerwall battery compare in energy storage to the battery in the electric cars?
- Suppose you wanted to charge your Powerwall battery with a stationary bike connected to a generator. If you could pedal and produce 100 Watts, how long would it take to charge?
- In his presentation, Elon Musk says that a small portion of the USA surface area could be used to provide solar power for the nation. Estimate the size of this square based on the power use for the USA and the power you get from the Sun. Also estimate the size of this area from the map that is shown in the presentation (I’m sure you can find a better image online). This is my kind of “trust but verify” question.
- Elon Musk also claims that the battery for the whole nation would just be a tiny red dot. Estimate the size of land you would need to store a day’s worth of energy.
- Tesla also announced the Powerpack. These are essentially industrial sized versions of the Powerwall that can store 100 kWh of energy. Musk also claims that with 160 million Powerpacks, you could move the USA to solar power with batteries. First, check this estimate of power storage. Second, how many Powerpacks would Telsa need to produce per day to make enough batteries to switch to solar in just one year.

via Wired