A small air bubble of initial radius r = 1 cm is introduced at the bottom of
a lake that is 20 m deep. The bubble expands as it rises slowly. Assume the lake
has the same temperature everywhere.
(a) What is the pressure at the bottom of the lake?
(b) What is the radius of the bubble after it rises to the surface?
Estimate (roughly) the net rate of heat loss by your body due to radiation when you are in a room with a temperature of 10 oC.
During phase transition, the change in the pressure P and temperature T can be expressed by the Clausius-Clapeyron relation,
dP/dT = L/(T ∆V),
where L is the latent heat and ∆V is the change in volume.
(a) How much pressure does one have to put on an ice cube to make it melt at -1o C?
The density of ice is 917 kg/m3, and the latent heat of 1 kg of ice melting is 333000 J.
(b) Approximately how deep under a glacier does it have to be before the weight of the ice above gives the pressure you found in part (a)?