Final answer:
The temperature difference of water between the top and bottom of Victoria Falls, considering a height of 63 meters, is approximately option B is correct answer.
Step-by-step explanation:
The question involves calculating the difference in temperature of water at the top and at the bottom of Victoria Falls, a height of 63 meters, using principles from energy conservation and thermodynamics. To find this temperature difference, we use the formula that equates gravitational potential energy lost to the thermal energy gained by the water. The gravitational potential energy (GPE) per unit mass (g*h) is equal to the specific heat capacity (c) times the mass (m) times the change in temperature (ΔT).
Since the mass cancels out on both sides of the equation, we get:
GPE = c * ΔT
Using g = 9.8 m/s² (acceleration due to gravity), h = 63 m (height of the falls), and c = 1 cal/g°C (specific heat capacity of water), we can calculate ΔT:
ΔT = gh / c
First, we convert the specific heat capacity to SI units by multiplying it by 4.2 J/cal (since 1 cal = 4.2 J) to get:
c = 1 cal/g°C * 4.2 J/cal = 4.2 J/g°C
Now, solving for ΔT:
ΔT = (9.8 m/s² * 63 m) / 4.2 J/g°C
ΔT = 623.7 J/g / 4.2 J/g°C
ΔT = 148.5°C/g
However, this value seems high due to a misunderstanding in the calculations. The correct assumption should be that the energy per unit mass given by gh should be equated to the product of the specific heat capacity of water and the change in temperature.
Therefore, the calculations should be redone correctly with J units for the potential energy and the specific heat. We obtain:
ΔT = (9.8 m/s² * 63 m) / 4.2 J/g°C
ΔT ≈ 0.147°C
So the correct difference in temperature of the water at the top and the bottom of Victoria Falls is approximately 0.147°C, which corresponds to option B.