How much does the temperature of a river rise in going over 30 m?

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Homework Help Overview

The problem involves calculating the temperature rise of a river as it flows over a 30 m waterfall, assuming no heat transfer with the surroundings and constant water velocity before and after the fall.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between potential energy and kinetic energy, questioning how energy conversion affects temperature. There are attempts to calculate potential energy and its implications for temperature change.

Discussion Status

The discussion is active, with participants exploring the energy transformations involved. Some calculations have been shared, and there is an ongoing examination of the assumptions regarding energy conversion and temperature rise.

Contextual Notes

There is uncertainty regarding the value of the coefficient of linear expansion (alpha) and how it applies to the problem. Additionally, the assumption of constant water velocity and the effects of turbulence are under consideration.

kingdomxiii
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Homework Statement


Assuming no heat is transferred to or from the surroundings, how much does the temperature of a river rise in going over a 30 m falls? (assume the velocity of the water is the same above and below the falls)

Homework Equations


Δl = αlΔT

The Attempt at a Solution


H = 0 and l = 30. I do not know where to go from there. I also do not know alpha.
 
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I presume that by "assume the velocity of the water is the same above and below the falls" you mean after that part of its energy has been turned into heat by the turbulence and contact with the rocks and bottom?

What is the potential energy of, say, 1 kg of water 30 ft m above the bottom of the falls? What is the increase in its kinetic energy at the bottom? What temperature difference does that energy convert to?
 
So I calculated the potential energy to be 294 Joules. So would the increase in kinetic energy equal 30?
 
kingdomxiii said:
So I calculated the potential energy to be 294 Joules. So would the increase in kinetic energy equal 30?
No. The decrease in potential energy would be equal to the increase in kinetic energy. If all this kinetic energy were converted to heat, how much would the temperature of the 1 kg of water rise?

Chet
 

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