Question

A scientist working late at night in her low-temperature 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 8.00 oz of water, at 12.0°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 31.3 cm.

 If she can complete 30 shakes per minute, how long will it take for the water to reach 77.1°C?

Answer 1

$Q_0=2mgh,$

$Q=nQ_0=cm∆t,$

$n=\frac{cm∆t}{2mgh}=\frac{c∆t}{2gh},$

$T=\frac n{T_0}=\frac{c∆t}{2ghT_0}=24.7^h.$