1. (25 pts.) If we have a house wall consisting of 12.0 cm of brick
(thermal conductivity k = 0.70 W/mK) on the outside and 4.0 cm of
fiberglass
insulation (thermal conductivity k unknown) on the inside, and we can
safely
ignore any other wall components in this calculation, then after drawing
a sketch of the wall determine the rate of heat loss [H] in W/m2 (that
is, let A = 1 m2) for this wall and the thermal conductivity [k] in W/mK
of the fiberglass insulation, assuming the inside temperature to be
25°
C. and the outside temperature to be
20° C, respectively, and the
temperature of the interface between the brick and the fiberglass
5° C.
2. (25 pts.) A sample of helium gas contains 3.0115 x 1024
atoms. (NA
= 6.023 x 1023)
(a) Determine the mass of the sample in grams.
(b) Find its volume at STP--standard temperature
(0° C.) &
standard pressure (1 atm).
(c) If the pressure increases to a value of 5 atm, while the
temperature
is decreased to
182° C., then determine the new volume of this same sample.
(d) Suppose now that the container for this sample of helium
gas develops
a leak overnight while it is fixed at a constant volume.
If the gauge
pressure of the container drops from 9 to 4 atm during this
period while
the temperature drops from 27 to
insulation
to be
3° C., then determine the percentage
of the original gas still remaining.
3. (25 pts.) (a) A sample of 3 moles of an ideal gas expands
isothermally
such that its volume doubles. What happens to its pressure
and its internal energy?
(b) If the same gas sample expands adiabatically instead, and
does 40 J of work during the expansion, determine the change in
internal
energy (include sign also).
(c) If the same gas sample expands isobarically instead, at 1
atm (1.013 x 105 Pa), then determine the net work done by the gas if the
volume changes from 10 L to 20 L.
(d) If a heat engine operates in a cycle between the fixed input
and output temperatures of 100°C and 0°C, determine the
maximum
possible efficiency.
(e) If 500 J of work are to be done by this engine, determine
the heat input to this system, assuming it is operating at the
maximum
efficiency found in part (d).
4. (25 pts.) A 4-gram string of length 3 m is fixed at both ends, and
standing waves are generated in the string. The value of the
tension in the string is 20 N.
(a) If the whole string vibrates in 3 loops, find the wavelength of
the waves in the string. Identify the harmonic and overtone number
of this vibration and sketch it.
Label clearly the positions of all nodes and antinodes in your sketch.
(b) Determine the wave velocity in the string.
(c) Determine the frequency of vibration for the mode of vibration
given
in part (a).
(d) What is the fundamental frequency of vibration?