Water drops from a waterfall 84 meters high .The temperature of the water at the bottom is found to be 26.2 degrees Celsius. Calculate its temperature at the top of the waterfall
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To calculate the temperature of the water at the top of the waterfall, we need to consider the concept of potential energy and its conversion to thermal energy.
The potential energy of an object is given by the formula:
PE = mgh
where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height.
In this case, the water drops from a height of 84 meters, so the potential energy it possesses at the top of the waterfall is:
PE = mgh = m * 9.8 * 84
To find the temperature at the top, we need to consider the principle of conservation of energy. The potential energy is converted into thermal energy at the bottom of the waterfall.
The thermal energy gained by the water can be calculated using the formula:
Q = mcΔT
where Q is the thermal energy, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.
In this case, the temperature changes from an unknown initial value (Ti) at the top to 26.2 degrees Celsius at the bottom.
Now, we equate the potential energy to the thermal energy gained:
PE = Q
m * 9.8 * 84 = m * c * (26.2 - Ti)
Simplifying the equation, we can cancel out the mass (m):
9.8 * 84 = c * (26.2 - Ti)
Solving for Ti, we rearrange the equation:
Ti = 26.2 - (9.8 * 84) / c
The specific heat capacity of water is approximately 4.18 J/g°C. Plugging in this value, we can calculate the temperature at the top of the waterfall using the equation above.