Thermo question...?

Question

I got through just about all of the problems with the exception of this last one.

A water parcel of mass m and initial temperature 15 C falls over a waterfall that is 100m high. Calculate the change in temperature, change in specific entropy, and amount of energy per unit mass degraded during the fall.

I can calculate the change in entropy using the standard s = -dQ/dT relationship once I find the change in temperature. Where I'm actually stuck is figuring out how to calculate the change in temp. and the amount of energy degraded. Would I use the first law?

I asked this in the Physics category and someone said to use U = mgh and then to factor in the specific heat of water, but I'm not sure how I'm supposed to use that. Am I letting Q = mgh??? Then the masses would cancel and you'd get 980 = (4186)(T2-T1).

But Q is heating and U is gravitational energy. So I'm confused.

Answer 1

This seems to be a question about conversion of one type of energy into another. In this case, gravitational potential energy (Ep) is converted to kinetic energy (Ek), and then to thermal energy (Q).

The loss of gravitational potential energy when it falls
delta Ep = mg(delta h)
where m is the mass of the object, g is the gravitational force constant 9.81 N/kg, and delta h is the change in height, is equal to its increase in kinetic energy.

I don't really believe that the kinetic energy is entirely converted to thermal energy, but if you assume that it is,
Q = m (deltaT)c
where m is the mass of the water being heated, delta T is the change in temperature, and c is the specific heat capacity of water (4.184 J/goC)

So, if delta Ep = Q

then mg(deltah) = m (deltaT) c

and (deltaT) = g (delta h)/c


Good luck !