Question

A 5.0-m-diameter garden pond is 30 cm deep. Solar energy is incident on the pond at an average rate of 400 W/m2 . If the water absorbs all the solar energy and does not exchange energy with its surroundings, how many hours will it take to warm from 15°C to 25°C?

Short answer

There will be a requirement for 8.7 hours will it take to warm from 15°C to 25°C

Step-by-step solution

Description 

A 5.0-m-diameter garden pond is 30 cm deep.

Solar energy is incident on the pond at an average rate of 400 W/m2 .

Thus$P=\frac{Q}{t}\Rightarrow t=\frac{Q}{P}$

Result of finding required hours 

Density of water:
$m=pV=pAh$

Needed heat:

$Q=cm∆T$

After combining:

$t=\frac{cm∆T}{P}=\frac{cpAh∆T}{P}=cph∆T\frac{1}{P/A}$

Therefore on the basis of numerical order:

$t=4190·1000·0.3·(25-15)·\frac{1}{400}=31425$

After converting into hours,

t =8.73 h

Therefore, there will be a requirement for 8.7 hours will it take to warm from 15°C to 25°C .