Assignment 6

Problem 1:

A tankless water heater heats water as it flows through the device.  The water circulates through a copper heat exchanger.  For a particular water heater the flow rate is 8.7 liter per minute.  The temperature rise of the water is 25 oC.   The water heater uses gas to heat the water in the copper coils and is 80% efficient.  What is the gas energy input rate in units of kW?
conversion:  1 kcal = 4186 J

Solution:

Problem 2:

Particles evaporating in the z-direction from a hole in a container with an ideal gas at temperature T.
(a)  Compute the speed distribution, f*(v), of the evaporating particles.  
(b)  Compute the mean z-component of the velocity, <vz>* of the escaping particles.
(c)  Compute the mean energy of the particles leaving the container.
Assume that the equilibrium in the interior of the container is not disturbed by the evaporating particles.

Maxwell-Boltzmann speed distribution:  f(v) = (m/(2πkT))3/2 4πv2exp(-mv2/(2kT)

Solution:

Problem 3:

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?

Solution:

Problem 4:

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.

Solution:

Problem 5:

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)?

Solution: