Question

The Sun delivers roughly 1 kW m(^(-2)) of power to the Earth's surface. A parabolic mirror with a 1 m radius is used to focus this energy onto a beaker containing 1 L of water. Estimate the time taken by the mirror to raise the temperature of the water by 50°C, assuming the specific heat capacity of water to be 4200 J K(^(-1))kg(^(-1)) and ignoring energy losses to the surroundings.

a) 120 seconds

b) 240 seconds

c) 360 seconds

d) 480 seconds

Answer 1

The time taken by the mirror to raise the temperature of the water by 50°C is approximately 1 second.

Step-by-step explanation:

To estimate the time taken by the mirror to raise the temperature of the water by 50°C, we can use the equation Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

First, let's calculate the heat energy Q using the equation Q = Pt, where P is the power delivered by the Sun and t is the time taken. Given that the power delivered by the Sun is 1 kW/m² and the area of the mirror is πr², where r is the radius of the mirror, we can calculate the power delivered by the mirror as P = 1 kW/m² * π * (1 m)².

Next, we can rearrange the equation Q = mcΔT to solve for t. Substituting the values we have, we get t = Q / (P * c * ΔT). Plugging in the values, we find t = 4200 J K⁻¹ kg⁻¹ * (50°C * 1 L * 1 kg/L * 1000 g/kg) / (1 kW/m² * π * 1 m² * 50°C).

Simplifying the equation, we find t = 0.707 seconds, which is approximately 1 second.