Water falls from a height of 84 m. Assuming that all the energy is converted into heat, the rise in temperature of water will be (4200 J/(kg °C) and g=10 m/s2)?
C∆T=gH
C of water=4200 J/kg°C
4200(T2-T1)= 10×84
T2-T1=10×84/4200
T2-T1=0.2°C
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To calculate the rise in temperature of the water, we need to use the principle of conservation of energy. The potential energy of the water at the top is converted into heat energy when it falls.
The potential energy of an object can be calculated using the formula:
Potential Energy = mass * acceleration due to gravity * height
In this case, the mass of water can be calculated using its density:
Density of water = mass / volume
Since the volume of water is not given, we assume a known value for the density of water, which is approximately 1000 kg/m³.
Density = 1000 kg/m³
We can rearrange the formula to find the mass of water:
Mass = density * volume
Now, let's calculate the mass of water:
Mass = 1000 kg/m³ * volume
Since volume is not given, we need to find it using the formula:
Volume = height * base area
The base area is not given, but assuming a simple shape like a cylinder, we can calculate the volume using the formula:
Volume = π * radius² * height
Assuming a radius of 1 meter, we can calculate the volume:
Volume = π * 1² * 84
Now that we have the volume, we can calculate the mass:
Mass = 1000 kg/m³ * volume
Using the mass, we can calculate the potential energy:
Potential Energy = mass * acceleration due to gravity * height
Now we can determine the rise in temperature of the water using the specific heat capacity formula:
Rise in Temperature = Potential Energy / (mass * specific heat capacity of water)
Using the known specific heat capacity of water (4200 J/(kg °C)), we can calculate the rise in temperature.
They want you to use
C= 4200 J/ kg*degC for the specific heat and
g = 10 m/s^2 for the acceleration of gravity
H = 84 m is the height
Energy conservation tells you that
C*(deltaT) = g*H
Solve for deltaT, in degrees C