Science of Submarines

1
Science of Submarines

• The Dallas

2
Dallas Submarine
3
Module Objectives

• Learn about the nuclear submarine Dallas, its
  history and its service.
• Learn about radioactive decay, as it applies to
  nuclear activity from the USS Dallas, and the
  mathematical equation (exponential decay)
  equation that models it.
• Learn about other applications of the exponential
  decay equation.

4
Submarine Science-Nuclear Decay

• Nuclear submarines rely on the nuclear decay
  of radioactive elements to power their reactors.
  Examining nuclear decay is an important area to
  study because it leads to an understanding of the
  safety and the high maintenance standards
  involved with the design, construction and
  operation of nuclear submarines.
• Nuclear decay on a submarine

5
Some Background atoms

• All matter in the universe is made up or composed
  of one or a combination of 108 presently known
  elements.
• An atom is smallest unit of a chemical element
  that can still retain the properties of that
  element. Atoms combine to form molecules.

6
Some Background atoms

• An atom has a dense central core (nucleus)
  consisting of positively charged particles
  (protons) and uncharged particles (neutrons).
• Negatively charged particles (electrons) are
  scattered in a relatively large space around this
  nucleus and move about it in orbital patterns at
  extremely high speeds

7
Atoms/Isotopes

• An atom contains the same number of electrons and
  protons and is electrically neutral.
• Isotopes are atoms of the same element with
  different masses. Isotopes have the same number
  of protons but a different numbers of neutrons in
  their nuclei.
• Isotopes of atoms that occur in nature are either
  stable and unstable (radioactive).

8
Radioactive Decay

• When an radioactive isotope breaks apart, it
  decays releasing radiation in the form of
• alpha particles, beta particles, and gamma
  rays.
• The scientific principle governing this type of
  decay process is
• The rate at which a radioactive material
  decays is proportional to the amount of the
  material present.

9
Radioactive Decay

• If A(t) denotes the amount of radioactive
  material at some time t, our scientific
  prin-ciple can be written in the mathematical
  form
• (rate of decay of A(t)) - k A(t)
• where k is the decay rate.
• This equation can be solved for A(t) to give
• A(t) A0e-kt
• where A0 is the original amount of material.
• Decay curves

10
Half-Life/Decay Rate

• Half-life, t1/2, is a commonly-used predictor of
  the decay activity of a radioactive isotope.
• Half-life is defined to be the amount of time
  for half of the atoms of an isotope to decay.
• The decay rate, k, of a radioactive material is
  related to the half-life by k 0.6931/t1/2.
• Decay curves

11
Radioactive Dating

• Problem Radioactive dating is a method for
  determining the age of various materials and is
  used to date samples ranging from a few years to
  billions of years. 14C is a radioactive isotope
  of carbon with a half-life of 5720 years and is
  taken up by every living thing. Below, the decay
  history of one gram of 14C is tabulated in
  50-year intervals for 5750 years k 0.6931/5720
  0.000121.
• Radioactive dating

12
Newtons Law of Cooling

• Because we cant use radioactive materials
  in the classroom to demonstrate exponential
  decay, we study a process that exhibits the same
  kind of decay behavior Newtons Law of Cooling
• The rate at which the temperature of an
  object changes is proportional to the difference
  between its own temperature and the tempera-ture
  of its surroundings.

13
Newtons Law of Cooling

• Denote the temperature of the object by Tobj and
  the temperature of the surrounding medium by Tmed
  
• Define Trel Tobj - Tmed, the temperature of the
  object relative to the temperature of the medium
• With k as the rate of temperature decay, our
  scientific principle can then be stated as
• (rate of change of Trel(t)) -kTrel(t)

14
A Cooling Probe

• A cup is filled with boiling water and a
  temperature probe is put into the water for one
  minute. The probe is taken out of the water and
  allowed to cool in the air with a CBL unit
  recording the temperature at five second
  intervals for about three minutes.
• Cooling probe

15
Glossary
16
References
17
Computational Problems