The sun outputs 1380 W/m^2 of energy at the earth's surface. A small rectangular las has the following dimensions: 1km wide, 1.4km long, and 300m deep
A) Calculate the thermal energy added to the lake if exposed to 12h of direct sunlight.
B) calculate the increase in temperature of the lake, assuming the temperature is even throughout.
Can someone please help me with both A & B please :)
Q =q•W•L•t= 1380•1000•1300•12•3600= =7.75•10¹³ J
Q=cmΔT
ΔT= Q/cm = Q/cρV=7.75•10¹³/4180•1000•1000•1300•300=
=0.048 K
Sure, I can help you with both parts A and B of your question.
A) To calculate the thermal energy added to the lake, we need to consider the amount of energy received from the sun and the time it is exposed to direct sunlight.
First, let's convert the dimensions of the lake into square meters:
Width = 1 km = 1000 m
Length = 1.4 km = 1400 m
Depth = 300 m
The surface area of the lake can be calculated by multiplying the width and length:
Surface Area = Width x Length = 1000 m x 1400 m = 1,400,000 m^2
Now, we can calculate the total energy received from the sun by multiplying the solar power output per square meter (1380 W/m^2) by the surface area of the lake:
Energy from the sun = Solar power output x Surface Area
Energy from the sun = 1380 W/m^2 x 1,400,000 m^2
Since the lake is exposed to direct sunlight for 12 hours, we need to multiply the energy by the time:
Thermal energy added to the lake = Energy from the sun x Time
Thermal energy added to the lake = (1380 W/m^2 x 1,400,000 m^2) x 12 hours
Calculating this will give you the thermal energy added to the lake over 12 hours.
B) To calculate the increase in temperature of the lake, we need to consider the specific heat capacity of water and the mass of the lake.
The specific heat capacity of water is approximately 4.18 J/g°C, which means it takes 4.18 Joules of energy to raise the temperature of 1 gram of water by 1 degree Celsius.
To calculate the mass of the lake, we need to multiply the volume of the lake by the density of water (assumed to be 1000 kg/m^3):
Volume of the lake = Width x Length x Depth
Volume of the lake = 1000 m x 1400 m x 300 m
Mass of the lake = Volume of the lake x Density of water
Mass of the lake = (1000 m x 1400 m x 300 m) x 1000 kg/m^3
Now, we can calculate the increase in temperature by dividing the thermal energy added to the lake (from part A) by the mass of the lake and the specific heat capacity of water:
Increase in temperature = Thermal energy added to the lake / (Mass of the lake x Specific heat capacity of water)
Calculating this will give you the increase in temperature of the lake assuming the temperature is even throughout.
Note: Please make sure to convert units consistently throughout the calculations.