Answer
16 minutes for the photovoltaic panel, 3.3 minutes for the mirror.
Work Step by Step
Calculate the energy required to heat the water, equation 14–2.
$$Q=mc\Delta T=(1.0kg)(4186 J/(kg \cdot C^{\circ})(70 C^{\circ}))=2.9302\times10^5 J$$
Use $1000 W/m^2$ as an estimate of the intensity of sunlight at the Earth’s surface. The 20 percent efficient photovoltaic panel has this power:
$$\frac{Q}{t}=(1000W/m^2)(1.5m^2)(0.20)=300J/s$$
We divide the required energy by the power to find the time.
$$t=\frac{Q}{Q/t}=\frac{2.9302\times10^5 J }{300J/s}=977s\approx 16 m$$
The curved mirror is 100 percent efficient, so it has this power:
$$\frac{Q}{t}=(1000W/m^2)(1.5m^2) =1500J/s$$
We divide the required energy by the power to find the time.
$$t=\frac{Q}{Q/t}=\frac{2.9302\times10^5 J }{1500J/s}=195s\approx 3.3 m$$
