A scientist working late at night in her lowtemperature...

A scientist working late at night in her lowtemperature physics laboratory decides to have a cup of hot tea, but discovers the lab hot plate is broken. Not to be deterred, she puts about 8 oz of water, at $12^{\circ} \mathrm{C}$, from the tap into a lab dewar (essentially a large thermos bottle) and begins shaking it up and down. With each shake the water is thrown up and falls back down a distance of $33 \mathrm{cm} .$ If she can complete 30 shakes per minute, how long will it take for the water to reach $87^{\circ} \mathrm{C} ?$ Would this really work? If not, why not?

Key Concepts

Gravitational Potential Energy

This is the energy an object possesses because of its position within a gravitational field. In the problem, the water is repeatedly lifted to a height (33 cm), and its potential energy is converted into kinetic energy as it falls. This energy conversion is a key step in examining whether the mechanical work of shaking can provide enough thermal energy to heat the water.

Mechanical Work and Energy Conversion

Mechanical work is done when a force is applied to move an object over a distance. When the scientist shakes the water, she performs work on it; this work is in principle converted into other forms of energy, such as kinetic and eventually thermal energy. This concept is pivotal in analyzing how external mechanical energy might increase the temperature of the water, and it opens discussion about the efficiency of this conversion.

Specific Heat Capacity

Specific heat capacity is the amount of energy required to raise the temperature of a unit mass of a substance by one degree Celsius. For water, this is a relatively high value, meaning a large amount of energy is necessary to significantly change its temperature. This concept helps quantify the energy needed to heat the water from 12°C to 87°C.

Efficiency of Energy Transfer

Real-world processes rarely convert energy from one form to another with perfect efficiency. When mechanical energy is converted to thermal energy, some of it is lost to other forms such as sound and friction. This inefficiency means that in practical scenarios like the one described, the energy supplied by shaking would not entirely go into heating the water, explaining why the method is unlikely to be effective.

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