How Much Warmer Could Water Get After a 50 Meter Fall?

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SUMMARY

The discussion centers on James Joule's experiment measuring the temperature change of water after a 50-meter fall. Using the equation for change in internal energy, ΔE = mgh, participants clarify that mass is not required for the calculation. The maximum expected temperature at the bottom of the fall is 10.0 degrees Celsius plus an increase of 0.117 degrees Celsius, resulting in a final temperature of 10.117 degrees Celsius. This conclusion is derived from the relationship between mechanical energy and thermal energy, emphasizing the conversion of gravitational potential energy into internal energy.

PREREQUISITES
  • Understanding of gravitational potential energy (mgh)
  • Familiarity with the concept of internal energy
  • Knowledge of specific heat capacity and its role in temperature change
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the principles of energy conservation in mechanical systems
  • Learn about specific heat capacity and its calculation
  • Explore the relationship between gravitational potential energy and thermal energy
  • Investigate Joule's experiments and their implications in thermodynamics
USEFUL FOR

Students in physics, educators teaching energy conversion concepts, and anyone interested in thermodynamics and mechanical energy applications.

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Homework Statement


On his honeymoon, James Joule tested the conversion of mechanical energy into internal energy by measuring temperatures of falling water. If water at the top of a Swiss waterfall has a temperature of 10.0 degrees Celsius and then falls 50.0 m, what maximum temperature at the bottom could Joule expect?


Homework Equations



change in internal energy = mgh


The Attempt at a Solution



I'm sure this question is easy I must be missing something, the change in internal energy is mgh but we have no mass?

The answer is (10.0 + 0.117) but I don't see how this was found.
 
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use
<br /> \Delta E = c M \Delta T<br />
where c is the specific heat. the mass drops out.
 

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