How Long Will it Take to Heat Water Using a Solar Heater?

[Jefffff]

Homework Statement

A solar heater is used to warm 150 kg of water by 30 K. The intensity of solar radiation is 6000 Wm^-2 and the area of the panels is 4.0 m². The specific heat capacity of the water is 4.2 * 10³ J/kg/K. Estimate the time this will take, assuming a solar panel efficiency of 60%.

Homework Equations

E=mcΔT

The Attempt at a Solution

Since there are 4 metres squared of solar panel and an efficiency of 60%:

6000 x 0.6 x 4 = 14400 W

The amount of energy needed to heat the water is:

E = mcΔT = 150 x 4.2 x 10^3 x 30 = 1.89 x 10^7 J

Therefore the time it will take is (1.89 x 10^7 J) / 14400 W = 1312.5 s = about 22 minutes.

In the answer sheet it says 3.6 hours, so I'm not sure where I went wrong.

Any help is appreciated!

 

[gneill]

The given value for solar radiation looks rather high. The Solar Constant is only between 1300 and 1400 W/m² at the top of the Earth's atmosphere. Perhaps there are unmentioned reflectors to gather more sunlight on the panels?

Otherwise, your calculation appears to be correct for the data given.

Perhaps the answer sheet has a typo (misplaced decimal point in the result). 1312 seconds is about 0.36 hours.

 

[Jefffff]

Ok, thanks!