Arthur Clarke wrote an interesting short story called “A Slight Case of Sunstroke.” Disgru...

The time taken to raise the temperature of the water in the cylinder to will depend on the total power reflected by the mirrors and the heat energy absorbed by the water in the cylinder. The amount of the power reflected by the mirrors depends on the intensity of solar radiation, and effective area. The absorbed heat energy of water will depend on the mass of the water, specific heat capacity and the temperature difference.

SKETCH:

The sketch for the given problem is shown in the below figure.

RESEARCH:

The amount of power reflected by mirror is given by the equation

Here, the intensity of the solar radiation,

From the above diagram, the effective area is given by

Here, the area of the mirror,

The angle of the mirror with the horizontal,

Therefore, the power reflected by the mirror becomes as

Now, the total power reflected by all the mirrors is

Here, the number of the mirrors,

The heat energy required to increase the water temperature to is given by the equation

Here the mass of the water,

The specific heat of the water,

The initial temperature of the water,

SIMLIFY:

Therefore, the time taken to raise the temperature of the water is given by …… (1)

CALCULATE:

Now, substituting the numerical values in the equation (1), we get ‘’