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 can use the concept of conservation of energy.
First, let's calculate the potential energy the water possesses at the top of the waterfall. The potential energy (PE) is given by the formula:
PE = m * g * h
where m is the mass of the water, g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the waterfall.
In this case, the mass of the water is given as 1 kg, and the height of the waterfall is 55 m. Substituting these values into the formula, we have:
PE = 1 kg * 9.8 m/s^2 * 55 m
= 539 J
The potential energy at the top of the waterfall is 539 Joules.
According to the law of conservation of energy, this potential energy is converted into other forms of energy as the water falls. One of these forms is thermal energy, which determines the temperature of the water.
To calculate the temperature difference, we need to know the specific heat capacity of water (c). The specific heat capacity of water is approximately 4.18 J/(g°C).
Since the mass of the water is given as 1 kg, we can convert this to grams by multiplying by 1000:
1 kg = 1000 g
Now, let's calculate the temperature difference between the water at the top and bottom of the waterfall using the formula:
ΔT = PE / (m * c)
where ΔT is the temperature difference, PE is the potential energy, m is the mass of the water, and c is the specific heat capacity of water.
Substituting the values into the formula, we have:
ΔT = 539 J / (1000 g * 4.18 J/(g°C))
≈ 0.129°C
Therefore, the temperature difference between the water at the top and bottom of the waterfall would be approximately 0.129°C.