23 November 1982
#1. It requires 80 cal of heat energy to raise the temperature of
50 gm of
a certain substance from 20 oC to 35 oC. The
substance has a molecular weight of 87 gm/mole. Its specific heat [in
cal/(gm oC) ] is most nearly equal to
#2. For the substance in problem #1, the molar specific heat [in cal/(mole oK) ]
is most nearly equal to
#3. Two metal rods, A and B, are joined end-to-end.
See sketch. They have equal cross-sectional areas. The left end of
rod A is kept at 100 oC by contact with boiling water,
while the right end of rod B is kept at 0 oC by contact
with an ice-water mixture. The thermal conductivity of rod A is 3
times that of B, but it is only half as long as B. After
steady state conditions have been reached, it is found that 3.5 gm of ice
is melted every 7.0 minutes. If the heat of fusion of ice is 80
cal/gm, then the rate at which heat is conducted through the rods (in cal/sec)
is most nearly equal to
#4. A weather balloon is filled with 9.00 m3 of He
under a pressure of 1.05 atm. It is released from the earth's
surface, where the temperature is 90 oF. The balloon
rises to an altitude where the temperature is -5 oF and the
pressure of the He is 0.95 atm. The volume [in m3]
of the Helium balloon is most nearly equal to
#5. A Gas begins with a pressure of 8.0 ´ 105
Pa, a volume of 0.0100 m3, and a temperature of 400 oK.
It expands isothermally to a volume of 0.0800 m3.
The work (in Joules) done by the gas is most nearly equal to
#6. Oxygen molecules have a molecular weight of 32 amu. At
room temperature (20 oC) the average translational kinetic
energy ( in Joules) of oxygen molecules is most nearly equal to
#7. A gas undergoes the processes indicated by the path in the p-V diagram ABCA. The
work (in Joules) done by the gas during one cycle is most nearly equal to
#8. In problem #7, the heat (in cal) removed from the gas
during one cycle, ABCA, is most nearly equal to
#9. Two moles of an ideal, diatomic gas undergoes an increase in
temperature by 40 oK, isobarically. The heat energy
added to the gas is most nearly equal to
( R = ideal gas constant)
#10. For the gas in problem #9, the work done by the gas is most
nearly equal to
#11. A fixed amount of gas with
g = 1.50, pressure of 6.0 atm. and volume of
1.0 liter is expanded
adiabatically to a volume of 4.0 liter. The pressure (in atm) of
the gas is then most nearly equal to
#12. Nitrogen molecules have a diameter of 3.2 ´ 10-8 cm.
At a low pressure in the container, the density of nitrogen is 2.4 ´ 1016
molecules/cm3 , and the rms speed is 2.0 ´ 105
cm/sec. The number of collisions per second which nitrogen molecules
undergo is most nearly equal to
#13. A hole is drilled through the earth's crust to a depth where the
temperature is 700 oC. A liquid is circulated to this
depth and is brought back to the surface as a gas at a temperature of 600oC.
The gas then does work in an engine where it is exhausted at 120oC.
The theoretical efficiency of the engine
14. An engine burns fuel (6000 cal/gm) at the rate of 4.0 gm/min.
The temperature of its working substance is 500 oK before
delivering its energy to the engine, and it is exhausted from the engine at 350
oK. The maximum theoretical power (in watts)
generated by the engine is most nearly equal to
#15. During the isothermal expansion (T = 400 oK) in a
Carnot engine, 440 cal of heat is absorbed by the working substance, and 330
cal is rejected during the isothermal compression at 300 oK.
The change in entropy ( in cal/oK) of the working substance
during one cycle is most nearly equal to