Physics
Thermodynamics
Water falls in a stream from a height of 21m. What is the rise in temperature of the water?
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Water falls in a stream from a height of 21m. What is the rise in temperature of the water?
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To determine the rise in temperature of the water, we need to equate the potential energy lost by the water to the heat gained by the water.
The potential energy (PE) lost by the water is given by:
- PE = mgh
where:
- m is the mass of the water
- g is the acceleration due to gravity (approximately 9.8 m/s²)
- h is the height from which the water falls (21 m)
The heat (Q) gained by the water is given by:
- Q = mcΔT
where:
- c is the specific heat capacity of water (approximately 4186 J/kg°C) (Engineering ToolBox)
- ΔT is the change in temperature
Equating the potential energy lost to the heat gained:
- mgh = mcΔT
We can cancel out the mass m from both sides of the equation:
- gh = cΔT
Now, solve for ΔT:
- ΔT = gh / c
Plugging in the values:
- ΔT = (9.8 m/s² * 21 m) / 4186 J/kg°C
- ΔT = 205.8 / 4186
- ΔT ≈ 0.049 °C
Therefore, the rise in temperature of the water is approximately 0.049°C.