James joule measures temperature of the water at the top and bottom of the waterfalls. If one of these waterfalls is 55m high, and all gravitation energy of the water is at the top of the falls. What temperature difference would be between the water at the top and bottom? (Consider mass of water as 1kg)
To determine the temperature difference between the water at the top and bottom of the waterfall, we need to consider the change in gravitational potential energy.
First, let's calculate the gravitational potential energy of the water at the top of the falls using the formula:
Potential Energy = mass * gravity * height
Given:
Mass of water = 1 kg
Height of waterfall = 55 m
Gravitational acceleration (gravity) = 9.8 m/s²
Potential Energy at the top = 1 kg * 9.8 m/s² * 55 m = 539 J
Since all the gravitational potential energy is at the top of the falls, this energy will be converted into heat as the water descends.
Now, let's convert this energy into temperature difference using the specific heat capacity of water.
The specific heat capacity of water is approximately 4.18 J/g°C.
To convert from joules to degrees Celsius, we can use the formula:
Energy = mass * specific heat capacity * temperature difference
Rearranging the formula to solve for temperature difference:
Temperature difference = Energy / (mass * specific heat capacity)
Temperature difference = 539 J / (1 kg * 4.18 J/g°C)
Temperature difference ≈ 129.19°C
Therefore, the approximate temperature difference between the water at the top and bottom of the waterfall would be around 129.19 degrees Celsius.