Exercise E6 Conversion: Energy, Power and Area
A Tesla Model 3 has an average power consumption of $ {{16~{\rm kWh}}\over{100~{\rm km}}}$ and an usable battery capacity of $60~{\rm kWh}$. Solar panels produces per $1~\rm m^2$ in average in December $0.2~{{{\rm kWh}}\over{{\rm m^{2}}}}$. The car is driven $50~{\rm km}$ per day. The size of a distinct solar module with $460~{\rm W_p}$ (Watt peak) is $1.9~{\rm m} \times 1.1~{\rm m}$.
1. What is the average power consumption of the car per day?
\begin{align*}
{{W}\over{l}} &= {{16~{\rm kWh}}\over{100~{\rm km}}} = 0.16 {{~{\rm kWh}}\over{~{\rm km}}} \\
W &= 50~{\rm km} \cdot 0.16 {{~{\rm kWh}}\over{~{\rm km}}} = 8~{\rm kWh}
\end{align*}
\begin{align*}
W = 8~{\rm kWh}\end{align*}
2. How many square meters (=$\rm m^2$) of solar panels are needed on average in December?
\begin{align*}
A = {{8~{\rm kWh}}\over{0.2 {{~{\rm kWh}}\over{~{\rm m^{2}}}}}} = 40~{\rm m^{2}}
\end{align*}
\begin{align*}
A=40~{\rm m^{2}}
\end{align*}
3. How many panels are at least needed to cover this surface?
\begin{align*}
A_{\rm panel} &= 1.9~{\rm m} \cdot 1.1~{\rm m} = 2.1~{\rm m^{2}} \\
n_{\rm panels} &= {{A }\over{ A_{\rm panel }}}
= {{40~{\rm m^{2}}}\over{2.1~{\rm m^{2}/panel}}} \\
&= 19.04~{\rm panels} \rightarrow 20~{\rm panels}
\end{align*}
\begin{align*}
n_{\rm panels} = 20~{\rm panels}
\end{align*}
4. What is the combined $\rm kW_p$ of the panels you calculated in 3. ?
\begin{align*}
P &= 20~{\rm panels} \cdot 460~{\rm kW_p / panel} \\
&= 9'200~{\rm kW_p}
\end{align*}
\begin{align*}
P = 9'200~{\rm kW_p}
\end{align*}