Having lost power in the storm I decide to boil 0.4 kg of water for my coffee by shaking it in a thermos flask

Question

Suppose that I use tap water at 5°C and that the water falls 40cm each shake, and I shake it 30 times per minute. Neglecting any loss of thermal energy by the flask, how long must I shake the flask untill the water reaches 100°C

Answer 1

So if you think about this problem, where is the energy coming from to heat the water? It's the kinetic energy added with each shake. Assuming no loss of energy to any outside sources or the bottle itself, the kinetic energy added is fully responsible for the potential energy it has as it reaches its peak, as all the kinetic energy is converted to potential.

So the energy added with each shake is the potential energy at the top of the 40 cm fall. Asssuming the water than comes back to rest at the bottom, this extra energy is transferred into the pool of water as soon as it lands, increasing its temperature.

So what is the energy of this water at the top of its shake?

The potential energy is due to gravity so its absolute value is mgh. m = .4 kg, g = 9.8 m/s^2, h = 40 cm = .4 m. So you can solve for that.

Then you need to figure out how many shakes it'll take to heat up the water. You know that the water, by thermodynamics, heats up proportionally to the amount of energy added, and its effects are determined by the specific heat capacity.

Q = mc delta T

So using the energy you get, you can solve for the rise in temperature due to each shake. You know that it must rise 95 degrees celsius so you can solve for how many shakes it takes.

Then knowing that you shake it 30 times per minutes, divide the number of shakes you find by 30 to find out how many minutes it takes. That's a simple rate equation.  

Answer 2

OK so assume:

1. You lower the thermos "slowly" so that all the water collects on the top of the container.

2. You then "slowly" stop your motion and the center of gravity of the water falls 40cm.

3. All that potential energy is converted in to kinetic energy, then into heat when the water impacts on the bottom of the thermos.

4. No heat losses out of the thermos, and your arm movements do not introduce any additional energy into the system.

5. You've got 1 cup = 8 oz of water in the thermos.

6. Density of water is constant over the temp range.

and some constants:

Cp = 4.186 J / g-C

Density = 1000 kg/^3

1 oz = 0.00003 m^3

Mass of water = 8 oz * 0.00003 m^3/oz) * (1000 kg / m^3) = 0.24 kg

The energy of the water will increase EACH SHAKE as follows:

E = m * g * H (potential energy equation)

E = 0.24 * 9.8 * 0.4 = 0.94 J

Energy needed to raise the water temp 95 degrees is

E = m * Cp * (T2 - T1)

E = 0.24 * 4.186 * (95) * 1000 = 95,441 J (watch units here)

So number of shakes is just

# = 95441 / 0.94 = 101533; assume 30 shakes per minute, that means you need

T = 101533 / 30 = 3384 minutes, or

T = 3384 / 60 = 56 hours!

You must really want that coffee...

Answer 3

Rub two flasks together.