``QUICKIES''

(a)

[1992 Xmas] For an ideal gas the pressure and temperature are directly related to one of the following velocities of the gas molecules (underline the correct one):   i most probable velocity;   (ii) average velocity;   (iii) root-mean-square velocity;   (iv) maximum velocity.

(b)

[1994 Final] A special constant-temperature rocket engine heats up an ideal gas of ``fuel'' atoms of mass m to a fixed temperature T and allows them to escape through a small hole as ``exhaust.'' Which would impart a larger impulse to the rocket payload - a fuel of hydrogen atoms or the same total fuel mass of lead atoms? (Remember, the average kinetic energy of ideal gas atoms depends only on T and not on m.)

(c)

[1995 Final] For an ideal gas of N particles in thermal equilibrium, the mean internal energy depends on [encircle all correct answers]
i temperature (ii) pressure (iii) volume

(d)

[1996 Final] In the same room we have a mixture of helium gas, oxygen gas, etc. What is the ratio of the helium average velocity to that of the oxygen molecules?

(e)

[1997 Final] For an ideal gas the pressure and temperature are directly related to one of the following velocities of the gas molecules: [underline one]
(i) most probable velocity; (ii) average velocity; (iii) root-mean-square velocity; (iv) maximum velocity.

[1993 P115 Xmas]

(a)

What are the two fixed points on the thermodynamic scale (constant volume ideal gas thermometer scale)?

(b)

How much heat is required to warm 6.0 kg of ice (c=2220 J/kg-K) from $-10^\circ$C to $0^\circ$C (staying as ice)?

(c)

How much heat is given off if you freeze 0.3 kg of water initially at $30^\circ$C (c=4190 J/kg-K and L=333,000 J/kg)?

(d)

If 0.3 kg of water is dropped onto a 6 kg block of ice at $-10^\circ$C, what is the final temperature when equilibrium is reached, and how much ice and/or water is there?

States of Mind and the Heat of Thought [1995 Final] Consider the following grossly over-simplified model: A mind is a system ${\cal S}$ capable of N distinct thoughts, of which only $n \le N$ are actually held in memory at any given time. Any given thought is either in memory or not; there is no middle ground. Furthermore, each thought takes the same amount of ``mental energy" $\varepsilon$, so that a mind with a total available mental energy U will always have exactly $n = U/\varepsilon$ thoughts in memory. A specific set of n thoughts can be considered one ``fully specified state of mind" for ${\cal S}$. We shall make the further (rather insulting) assumption that every possible fully specified state of mind with n thoughts is a priori equally likely.

(a)

How many different fully specified states with n thoughts could occupy a mind which has ``mental room" for N thoughts?

(b)

What is the entropy $\sigma$ of a mind which has the capacity for 12 thoughts but currently contains only 4?

(c)

Explain how to define a mental temperature $\tau$ for a given mind, assuming only that you know how the number of possible fully specified states of that mind depends on its total mental energy. [The specific form of said dependence need not be the one you gave above.]

(d)

If ${\cal S}_1$, which has very little mental energy U₁ but a large mental temperature $\tau_1$, is free to exchange thoughts with ${\cal S}_2$, which has enormous mental energy U₂ but a small mental temperature $\tau_2$, whose mental energy is most likely to increase?  Explain. (Assume both are isolated mentally from the rest of the world.)

(e)

Now suppose that one particular mind is in ``mental equilibrium" with the UBC intellectual community, which we shall assume has a ``mental temperature" of $\tau = 1$ mJ. If it takes that mind an extra mental energy of $\varepsilon = 4$ mJ to have a given thought (in addition to whatever other thoughts it might be having), what is the probability of that specific thought being present in that mind at any given time?

[1992 P115 Xmas] A 180 g copper pot contains 200 litre of water at an initial temperature of 20$^{\circ}$C. A copper rod heated to 900 $^{\circ}$C is dropped into the water. This causes the water to boil with 5.0 g of water converted to steam. What is the mass of the copper rod?

Specific heat of copper = 386 J/kg.K

Specific heat of water = 4190 J/kg.K

Heat of vaporisation of water = 2256000 J/kg

[1992 P115 Xmas] An igloo, a hemispherical enclosure built of ice, has an inner radius of 2.5 m . The thickness of the ice is 50 cm. On a cold winter day the outside temperature is -40$^{\circ}$C. At what rate must thermal energy be generated to maintain the temperature inside the igloo at $-5^\circ$C?

Thermal conductivity of ice = 0.592 W/m$\cdot$K

A quantity of gas ( $\gamma = 1.4$) expands adiabatically and quasi-statically from an initial pressure of 2 atm and volume of 2 $\ell$ at temperature of 20$^{\circ}$C to twice its original volume.

(a)

What is the final pressure of the gas?

(b)

What is the final temperature of the gas?

-- FINIS -