A solar heating panel on a roof is used to heat 40 kg of water initially at 22 degress celsius, using the sun, which absorbs 750 joules per second. What would the temperature of this water be after 1 hour?
They need to tell you:
(1) if water is flowing through, and at what rate
(2) convective heat loss to the air.
(3) radiative heat loss
They probably expect you to assume no flow and neglect the loss terms. This will lead to a high prediction of the temperature rise. This is a poor way to teach physics, in my opinion.
Multiply 750 J/s by 3600 s. That will be the heat added to the water. Divide that by (Mass)x(specific heat) for the temperature rise.
To find the temperature of the water after 1 hour, we need to calculate the total amount of energy that is absorbed by the water and then use that information to calculate the final temperature.
First, we need to find the total energy absorbed by the water over the course of 1 hour. We know that the solar heating panel absorbs 750 joules per second.
To find the total energy absorbed, we multiply the energy absorbed per second by the duration in seconds:
Energy absorbed = 750 joules/second x 3600 seconds (1 hour) = 2,700,000 joules
Next, we need to calculate the change in temperature of the water using its specific heat capacity.
Specific heat capacity (C) is the amount of energy required to raise the temperature of a substance by 1 degree Celsius per unit mass.
The specific heat capacity of water (c) is 4186 J/kg·°C.
Now we can use the formula:
Energy absorbed = mass x specific heat capacity x change in temperature
Rearranging the formula to solve for the change in temperature, we have:
Change in temperature = Energy absorbed / (mass x specific heat capacity)
Plugging in the known values:
Change in temperature = 2,700,000 joules / (40 kg x 4186 J/kg·°C)
Performing the calculation, we get:
Change in temperature ≈ 16.21 °C
Finally, we can find the final temperature by adding the change in temperature to the initial temperature:
Final temperature = Initial temperature + Change in temperature
Final temperature ≈ 22 °C + 16.21 °C
Final temperature ≈ 38.21 °C
Therefore, after 1 hour, the temperature of the water would be approximately 38.21 degrees Celsius.