Complete Solutions Manual included
University Physics for the Life Sciences, 1st
edition Knight
ALL CHAPTERS
INCLUDED
, PHYSICS FOR THE LIFE SCIENCES
!"
QUESTIONS
Q1.1 REASON: We know from the reading that diffusion distances scale with the square root of time. Specifically,
Equation 1.3 tells us xrms = 2 Dt . So, if the time were quadrupled, we would expect the diffusion distance to
double from d to 2d .
ASSESS: This is not specific to one dimension. Equation 1.5 for three dimensions reads rrms = 6 Dt . It has a
different numerical constant, but the dependence on time is the same.
1
Q1.2 REASON: The diffusion constant is given by Equation 1.2, D = vd . The fact that Xenon atoms are heavier
2
won’t affect the distance between collisions very much, but the fact that they are slower means the diffusion
constant will be smaller for Xenon.
ASSESS: It is intuitive that a heavy, slow-moving thing will spread more slowly than a light, fast-moving
thing.
Q1.3 REASON: We know that higher temperature indicates faster molecular motion on a microscopic scale. So, we
expect diffusion to be faster in hot water than in cold water. This means the diffusion constant will be larger
for hot water.
ASSESS: This can be seen easily by putting drops of food coloring or other dyes into glasses of water with
different temperatures.
Q1.4 REASON: One reason might be that the elephant trunk snake is larger. The surface area of skin available for
gas exchange scales with × r (treating the snake as cylindrical). The volume available for lungs scales with
× r 2 . So as snake size increases, the surface area increases linearly with r , whereas the volume increases
quadratically in r , meaning V ∝ r 2 . Thus, as snake size increases, volume increases faster than surface area,
and using the volume for lungs becomes more efficient than using the skin for gas exchange.
ASSESS: This is not the only possible reason. A larger snake may also have a thicker skin, such that diffusion
of gases through the skin would take longer for the larger snake.
1-1
University Physics for the Life Sciences, 1st
edition Knight
ALL CHAPTERS
INCLUDED
, PHYSICS FOR THE LIFE SCIENCES
!"
QUESTIONS
Q1.1 REASON: We know from the reading that diffusion distances scale with the square root of time. Specifically,
Equation 1.3 tells us xrms = 2 Dt . So, if the time were quadrupled, we would expect the diffusion distance to
double from d to 2d .
ASSESS: This is not specific to one dimension. Equation 1.5 for three dimensions reads rrms = 6 Dt . It has a
different numerical constant, but the dependence on time is the same.
1
Q1.2 REASON: The diffusion constant is given by Equation 1.2, D = vd . The fact that Xenon atoms are heavier
2
won’t affect the distance between collisions very much, but the fact that they are slower means the diffusion
constant will be smaller for Xenon.
ASSESS: It is intuitive that a heavy, slow-moving thing will spread more slowly than a light, fast-moving
thing.
Q1.3 REASON: We know that higher temperature indicates faster molecular motion on a microscopic scale. So, we
expect diffusion to be faster in hot water than in cold water. This means the diffusion constant will be larger
for hot water.
ASSESS: This can be seen easily by putting drops of food coloring or other dyes into glasses of water with
different temperatures.
Q1.4 REASON: One reason might be that the elephant trunk snake is larger. The surface area of skin available for
gas exchange scales with × r (treating the snake as cylindrical). The volume available for lungs scales with
× r 2 . So as snake size increases, the surface area increases linearly with r , whereas the volume increases
quadratically in r , meaning V ∝ r 2 . Thus, as snake size increases, volume increases faster than surface area,
and using the volume for lungs becomes more efficient than using the skin for gas exchange.
ASSESS: This is not the only possible reason. A larger snake may also have a thicker skin, such that diffusion
of gases through the skin would take longer for the larger snake.
1-1
