Kinetic Theory of Gases

Homework Assignment

From the FIFTH edition

Questions: 1, 2, 4, 6, 12, 15

Problems: *, 3, **, 8, 13, ****, 25, *****, ******, 33

Be sure and do these; do not just wait and watch me do them in class!

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Q21.1 Dalton's law of partial pressures states: The total pressure of a mixture of gases is equal to the sum of the partial pressures of gases making up the mixture. Give a convincing argument of this law based on the kinetic theory of gases.

Q21.2 One container is filled with helium gas and another with argon gas. If both containers are at the same temperature, which molecules have the higher rms speed?

Q21.4 Although the average speed of gas molecules in thermal equilibrium at some temperature is greater than zero, the average velocity is zero. Explain.

Q21.6 A liquid partially fills a container. Explain why the temperature of the liquid decreases when the container is partially evacuated. (It is possible to freeze water using this technique.)

Q21.12 Why does a diatomic gas have a greater thermal energy content per mole than a monatomic gas at the same temperature?

Q21.13 An ideal gas is contained in a vessel at 300 K. If the temperature is increased to 900 K,

(a) by what factor does the rms speed of each molecule change?

(b) by what factor does the pressure in the vessel change?

Problems: *, 3, **, 8, 13, ****, 25, *****, ******, 33

21.*. Find the rms speed of nitrogen molecules under standard conditions, 0.0oC and 1.00 atm pressure. Recall that 1 mole of any gas occupies a volume of 22.4 liters under standard conditions.

21.3 In a 30-s interval, 500 hailstones strike a glass window of area 0.60 m2 at an angle of 45o to the window surface. Each hailstone has a mass of 5.0 g (0.005 kg) and a speed of 8.0 m/s. If the collisions are elastic, find the average force and pressure on the window.

21.** Calculate the rms speed of an H2 molecule at 250oC.

21.8 If the rms speed of a helium atom at room temperature is 1350 m/s, what is the rms speed of an oxygen (O2) molecule at this temperature? (The molar mass of O2 is 32 and the molar mass of He is 4.)

21.*** One mole of xenon gas at 20.0oC occupies 0.0224 m3. What is the pressure exerted by the Xe atoms on the walls of a container?

21.13 Calculate the change in internal energy of 3.0 moles of helium gas when its temperature is increased by 2.0 K.

21.**** One mole of an ideal monatomic gas is at an initial temperature of 300 K. The gas undergoes an isovolumetric process acquiring 500 J of heat. It then undergoes an isobaric process losing the same amount of heat. Determine (a) the new temperature of the gas and (b) the work done on the gas.

21.25 Two moles of an ideal gas (gamma = 1.40) expands slowly and adiabatically from a pressure of 5.0 atm and a volume of 12.0 liters to a final volume of 30.0 liters. (a) What is the final pressure of the gas? (b) What are the initial and final temperatures?

21.***** Four liters of a diatomic ideal gas (gamma = 1.40) confined to a cylinder are put through a closed cycle. The gas is initially at 1.0 atm and at 300 K. First, it expands adiabatically to its original pressure and finally is compressed isobarically to its original volume.

(a) Draw a PV diagram of this cycle.

(b) Determine the volume at the end of the adiabatic expansion.

(c) Find the temperature of the gas at the start of the adiabatic expansion

(d) Find the temperature at the end of the cycle.

(e) What was the net work done for this cycle?

21.****** A 5.0-liter vessel contains 0.125 mole of an ideal gas at 1.50 atm. What is the average translational kinetic energy of a single molecule?

21.33 Consider 2.0 moles of an ideal diatomic gas. Find the total heat capacity at constant volume and at constant pressure if

(a) the molecules rotate but do not vibrate and

(b) the molecules rotate and vibrate.

Ch21 ToC

Molecular Model

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