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Earth receives solar energy at a rate of...

Earth receives solar energy at a rate of `1000 Wm^(-2)`. A solar water heater of area `2m^(2)` absorbs 50% of incident energy. Find the time required to raise the temperature of 50 litres of water by `50^(@)C`. `(C_(W)= 4180 J kg^(-1) K^(-1))`

Text Solution

Verified by Experts

For `2m^(2)`, rate= 2000W
Total energy absorbed in a time t second is `Q_(1)= 2000 xx (50)/(100) xx t= (1000 xx t)J`
Heat required to raise the temperature of 50 litres of water by `50^(@)C` is
`Q_(2)= mC_(w) Delta T= 50 xx 4180 xx 50`
`=1.045 xx 10^(7)J`
We have, `Q_(1)= Q_(2)`

`therefore 1000t = 1.045 xx 10^(7)`
`therefore t= (1.045 xx 10^(7))/(1000)= 10450s` or t=2 hr 54 min 10s
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