[SOLVED] Physics 230 Homework Set 5

CQ1. Consider two identical containers, one is filled with helium gas and the other is filled
with oxygen gas. Both gases are found to have the same root-mean-square speeds.
How do their temperatures compare? Answer quantitatively!CQ2. The average kinetic energy of the molecules in an ideal gas increases with the volume
remaining constant. Which of the following statements must be true?a) The pressure increases and the temperature stays the same.
b) The number density decreases.
c) The temperature increases and the pressure stays the same.
d) Both the pressure and the temperature increase.CQ3. The rms speed is the
a) speed at which all the gas molecules move.
b) speed of a molecule with the average kinetic energy.
c) average speed of the gas molecules.
d) maximum speed of the gas molecules.CQ4. If the temperature of an ideal gas is doubled and the pressure is held constant, the rms
speed of the molecules
a) remains unchanged.
b) is 2 times the original speed.
c) is p2 times the original speed.
d) is 4 times the original speed.P1. The mean free path of nitrogen molecules is 8.0108 m when the gas is held at a
temperature of 0.0C and a pressure of 1.0 atm. Calculate the diameter of the nitrogen
molecules.P2. Consider a 5-particle gas of molecules with velocities given by
~v1 = (15 25| + 25
k) m/s
~v2 = (20 30| + 40
k) m/s
~v3 = (35 + 20| 10
k) m/s
~v4 = (20 30| 30
k) m/s
~v5 = (20 + 65| + 25
k) m/s (1)Calculate the
a) average velocity,
b) the average speed, and
c) the root-mean-square speed of the gas particles.P3. A container of gas has a density of 1.24 105 g/cm3 when the pressure of the gas is
1.01 103 Pa and its temperature is 0.00C.
a) Calculate the root-mean-square speed of this gas?
b) Calculate the molar mass of the gas and identify the gas.P4. 8.5 g of oxygen gas, with an initial temperature of 325C is placed in thermal contact
with 3.5 g of helium gas, which has an initial temperature of 23C.
a) Calculate the initial and final thermal energies of each gas.
b) How much heat is transferred, and in which direction?
c) Calculate the final temperature.
d) Calculate the final pressure in each cylinder.P5. A monatomic gas is isochorically heated until the gas temperature triples. Do each of
the following quantities change? If so, do each increase or decrease, and by what factor.
If not, why not?a) The root-mean-square speed.
b) The mean free path.
c) The thermal energy of the gas.d) The molar specific heat at constant volume.P6. 1.00 mol of helium gas starts at an initial state A, which is characterized by a pressure
of 1.00 atm and a temperature 300.K. The gas undergoes an isochoric heating until
it reaches a state B where the gas reaches a temperature of 600.K. The gas then
undergoes an adiabatic expansion until it reaches a state C where the gas reaches its
initial pressure. Finally, the gas undergoes an isobaric compression, which brings the
gas back to its initial state A .a) Calculate the pressure and volume of the gas at states B and C.
A, B, and C, respectively.b) Draw a pV diagram showing this process. This diagram needs to include axes
labels and an arrow indicating the direction traversed between the initial and final
points on the pV curve. Also, indicate the temperature at each point.c) Calculate the heat, Q, work done on the gas, W, and thermal energy change, Eth
for the gas as it goes through each of the three aforementioned processes.