a waterfall is 122 m in height. calculate the rise in temperature if all potential lost is converted to heat.
To calculate the rise in temperature when all potential energy lost by a waterfall is converted to heat, we need to use the concept of potential energy and the specific heat capacity of water. Here's how you can calculate it:
Step 1: Determine the potential energy lost by the waterfall.
The potential energy (PE) of an object is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity (roughly equal to 9.8 m/s²), and h is the height.
In this case, we need to find the potential energy lost by the waterfall, so m is not required. Therefore, we can simplify the equation to PE = gh.
Given that the height of the waterfall is 122 m, we can calculate the potential energy lost as follows:
PE = gh
= (9.8 m/s²) × (122 m)
= 1195.6 J (Joules)
Step 2: Convert the potential energy lost to heat.
According to the law of conservation of energy, all the potential energy lost by the waterfall is converted to heat energy.
Step 3: Calculate the temperature rise using the specific heat capacity of water.
The specific heat capacity (c) of a substance is defined as the amount of heat energy required to raise the temperature of one gram of the substance by one degree Celsius.
For water, the specific heat capacity is approximately 4.186 J/g°C.
To calculate the temperature rise (∆T), we can use the formula:
∆T = Q / (mc)
Where Q is the heat energy, m is the mass, and c is the specific heat capacity.
Since we know the heat energy (Q) is the potential energy lost (1195.6 J) and the specific heat capacity (c) of water (4.186 J/g°C), we just need to find the mass (m) of the water.
Step 4: Determine the mass of the water.
We need to know the mass of the water flowing in the waterfall. Assuming that the water has a density of 1 g/cm³, we can calculate the mass as follows:
Density (ρ) = Mass (m) / Volume (V)
1 g/cm³ = m / (100 cm × 100 cm × 100 cm)
m = 1 g/cm³ × (100 cm × 100 cm × 100 cm)
m = 1000000 g
Step 5: Calculate the temperature rise.
Using the formula ∆T = Q / (mc), we can calculate the temperature rise as follows:
∆T = (1195.6 J) / (1000000 g × 4.186 J/g°C)
∆T ≈ 0.029 °C
Therefore, if all the potential energy lost by the 122 m waterfall is converted to heat, the temperature of the water would rise by approximately 0.029 °C.