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Chapter 19: Q. 39 (page 544)

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

Expert verified

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

Step by step solution

01

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 .

ThusP=Qt⇒t=QP

02

Result of finding required hours 

Density of water:
m=pV=pAh

Needed heat:

Q=cm∆T

After combining:

t=cm∆TP=cpAh∆TP=cph∆T1P/A

Therefore on the basis of numerical order:

t=4190·1000·0.3·(25-15)·1400=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 .

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