A water fall is 84 metre.If half of kinetic energy is converted into heat.What is the rise in the temperature of water?
Mgh=2Mc(change in temperature),where M is mass of water,g is gravitational acceleration,h is the height of waterfall,c is specific heat capacity of water.c=4200 J/Kg/K,g=10m/s^2.
.4 degree
To calculate the rise in temperature of the water, we need to make a few assumptions and use the conversion formula.
Assumptions:
1. We assume that the entire 84-meter waterfall height is converted into kinetic energy for the water.
2. We assume that the kinetic energy is evenly distributed throughout the water.
3. We assume that the water has a specific heat capacity of 4.18 J/g°C, which is the average value for water.
Formula for calculating the rise in temperature:
ΔT = (ΔE) / (m * c)
where:
ΔT = Rise in temperature (in °C)
ΔE = Change in energy (in J)
m = Mass of water (in g)
c = Specific heat capacity of water (in J/g°C)
First, we need to calculate the change in energy (ΔE) using the given information that half of the kinetic energy is converted into heat.
ΔE = (1/2) * (m * g * h) <-- Formula for kinetic energy, where g is the acceleration due to gravity and h is the height of the waterfall
Given:
h = 84 meters
g = 9.8 m/s² (approximate value for gravity)
Substituting the values:
ΔE = (1/2) * (m * 9.8 * 84)
Now, we can use the mass of the water to calculate the rise in temperature.
Since we don't have the mass (m) of the water, we'll need to make another assumption. Let's assume that the mass of the water is 1,000 grams (equivalent to 1 liter or 1 kilogram).
Substituting this value into the equation, we get:
ΔT = [(1/2) * (1000 * 9.8 * 84)] / (1000 * 4.18)
Simplifying the equation:
ΔT = 158760 / 4180
Calculating the value:
ΔT ≈ 38.01 °C
Therefore, the rise in temperature of the water will be approximately 38.01 °C.