How do you calculate the increase in temperature for the followingproblem? Water
ID: 1727658 • Letter: H
Question
How do you calculate the increase in temperature for the followingproblem?Water at the top of Niagara Falls has a temperatureof 11.0°C. If it falls adistance of 70.0 m and allof its potential energy goes into heating the water, calculatethe increase in temperature of thewater at the bottom of the falls.
Thanks,BuddyJ
Water at the top of Niagara Falls has a temperatureof 11.0°C. If it falls adistance of 70.0 m and allof its potential energy goes into heating the water, calculatethe increase in temperature of thewater at the bottom of the falls.
Thanks,BuddyJ
Explanation / Answer
OK, so when the water falls, it's potential energy is converted tokinetic energy. Then, when it lands, this kinetic energy goes tozero, and we are told that the energy goes into heating the water(actually, we are told that all of it's potential energy goes intoheating the water, but first it must fall, so actually thepotential energy is converted to kinetic energy, and then tointernal energy). Let's just focus on 1kg of water. It's potential energy at the topof the waterfall is P=mgh = 1kg*9.8m/s^2*70.0m ~ 700J (you shoulddo the calculation to get a more accurate number). This potentialenergy is converted completely to kinetic energy by the time thewater reaches the bottom (by conservation of energy), and then weare told that this energy goes into heating the water (it isconverted to internal energy of the water). So think of this asheat added to the water. Then use Q = mCT Q is the amount of energy which is added to the water (~700 J, justthe answer you found for the potential energy) C is the specific heat of water in J/(kg * degrees C) (=4186J/(kg*degrees C)) m is the mass of the water (1kg in this case) T is the change in temperature = T final - T initial we want to solve for T final so rearrange the above equation tofind T = Q/(mC) T final - T initial = Q/(mC) where T initial = 11 degrees C, so T final = Q/(mC) + T initial plug in the numbers and you will have your answer.
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