Thermodynamics: Time to Warm Garden Pond from 16.0C to 20.0C

[Wubz]

Homework Statement

A 5.0-m-diameter garden pond is 0.200 m deep. Solar energy is incident on the pond at an average rate of 400 W/m^2 . 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 16.0C to 20.0C?

Homework Equations

I'm have been using the equation Q/t = e * (5.67 * 10 ^ -11) * A *T^4
Not sure if this is correct.

The Attempt at a Solution

My lesser attempts assigned the radiated power to Q and I would solve for time, however I am pretty sure this is incorrect.

 

[Andrew Mason]

Homework Statement

A 5.0-m-diameter garden pond is 0.200 m deep. Solar energy is incident on the pond at an average rate of 400 W/m^2 . 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 16.0C to 20.0C?

Homework Equations

I'm have been using the equation Q/t = e * (5.67 * 10 ^ -11) * A *T^4
Not sure if this is correct.

This is a heat capacity question, not a radiation question. Use:

$$Q = mC\Delta T$$

where Q = Power x time

Hint: you have to work out the mass of the water in the pond and the rate at which solar heat energy is added to the pond.

AM