## Extra Credit 5

### Integrated concepts

In this extra credit exercise you are asked to connect concepts introduced in various modules to solve some physics problems.
If needed, use the constants and conversions with the precision shown below, to avoid rounding errors.

Boltzmann constant:  kB = 1.38*10-23 J/K  = 8.617* 10-5 eV/K
Elementary electric charge:  qe = 1.6 * 10-19 C
Gravitational acceleration g:  g = 9.8 m/s2

Specific heat capacities:
(kcal/(kgoC))

 Water 1 Ice 0.49 Steam 0.48 Glass 0.2 Steel 0.11 Copper 0.092 Aluminum 0.215

Latent heat (Water)   (kcal/kg)

 Latent heat of fusion 80 Latent heat of vaporization 540

Conversions:
1 eV = 1.6 * 10-19 J
1 kcal = 4186 J

Please work through the problems below and answer all the questions.  Then go to Canvas, Extra credit 5, and enter your answers to selected questions.
(The symbols in square brackets will be replaced by numbers in Canvas.)

#### Problem 1:

You ionize molecules of a gas by removing one electron and then accelerate them from rest through a potential difference of [V].
(a)  What is the kinetic energy of a gas molecular ion after it has been accelerated?
(b)  At what temperature will the average kinetic energy of molecules of that gas be the same as that of the accelerated ions?

#### Problem 2:

A lightning bolt strikes a tree, moving 30 C of charge through a potential difference of 80 MV.
(a)  What energy was dissipated?
(b)  What mass of water could be raised from 15 oC to the boiling of 100 oC and then completely vaporized  by this energy?
(c)  Discuss the damage that could be caused to the tree by the expansion of the boiling steam.

#### Problem 3:

A 12 V battery-operated bottle warmer heats [m1] g of glass, [m2] g of baby formula, and [m3] g of aluminum from 20 oC to 80 oC.
(a)  How much charge is moved by the battery?
(b)  How many electrons per second flow if it takes [t] min to warm the formula?
(Hint: Assume that the specific heat of baby formula is the same as the specific heat of water.)

#### Problem 4:

A battery-operated car utilizes a 12 V system.
Find the charge the batteries must be able to move in order to accelerate the [m] kg car from rest to [v] m/s while making it climb a [h] m high hill.

#### Problem 5:

The probability of fusion is greatly enhanced when appropriate nuclei are brought close together, but the mutual Coulomb repulsion must be overcome. This can be done using the kinetic energy of high-temperature gas ions or by accelerating the nuclei toward one another.
(a)  Calculate the potential energy of two singly charged nuclei separated by 10−12 m.
Hint find the potential of one point nucleus at a distance of 10−12 m, and then find the potential energy of the other nucleus by multiplying by its charge.
(b)  At what temperature will atoms of a gas have an average kinetic energy that is equal to this electrical potential energy?

Now go to Canvas, Assignments, Extra Credit 5 and answer questions 1 - 5.  You can submit twice and the highest score counts.