Additional Problems

| 46 | At the start of a trip, a driver adjusts the absolute pressure in her tires to be when the outdoor temperature is 284 K. At the end of the trip she measures the pressure to be . Ignoring the expansion of the tires, find the air temperature inside the tires at the end of the trip.

| 47 | ssm A young male adult takes in about of fresh air during a normal breath. Fresh air contains approximately 21% oxygen. Assuming that the pressure in the lungs is and air is an ideal gas at a temperature of 310 K, find the number of oxygen molecules in a normal breath.

| 48 | A frictionless gas-filled cylinder is fitted with a movable piston, as the drawing shows. The block resting on the top of the piston determines the constant pressure that the gas has. The height h is 0.120 m when the temperature is 273 K and increases as the temperature increases. What is the value of h when the temperature reaches 318 K?

| 49 | Review Conceptual Example 7 before working this problem. For water vapor in air at 293 K, the diffusion constant is . As outlined in Problem 44(a), the time required for the first solute molecules to traverse a channel of length L is , according to Fick’s law. (a) Find the time t for . (b) For comparison, how long would a water molecule take to travel at the translational rms speed of water molecules (assumed to be an ideal gas) at a temperature of 293 K? (c) Explain why the answer to part (a) is so much longer than the answer to part (b).

| 50 | Initially, the translational rms speed of a molecule of an ideal gas is 463 m/s. The pressure and volume of this gas are kept constant, while the number of molecules is doubled. What is the final translational rms speed of the molecules?

| 51 | ssm Suppose that a tank contains 680 m3 of neon at an absolute pressure of . The temperature is changed from 293.2 to 294.3 K. What is the increase in the internal energy of the neon?

| 52 | A tank contains 0.85 mol of molecular nitrogen (N2). Determine the mass (in grams) of nitrogen that must be removed from the tank in order to lower the pressure from 38 to 25 atm. Assume that the volume and temperature of the nitrogen in the tank do not change.

* | 53 | ssm Estimate the spacing between the centers of neighboring atoms in a piece of solid aluminum, based on a knowledge of the density (2700 kg/m3) and atomic mass (26.9815 u) of aluminum. (Hint: Assume that the volume of the solid is filled with many small cubes, with one atom at the center of each.)

* | 54 | The pressure of sulfur dioxide (SO2) is . There are 421 moles of this gas in a volume of 50.0 m3. Find the translational rms speed of the sulfur molecules.

* | 55 | Interactive Solution 14.55 at provides a model for problems of this type. The temperature near the surface of the earth is 291 K. A xenon atom has a kinetic energy equal to the average translational kinetic energy and is moving straight up. If the atom does not collide with any other atoms or molecules, how high up would it go before coming to rest? Assume that the acceleration due to gravity is constant throughout the ascent.

** | 56 | When perspiration on the human body absorbs heat, some of the perspiration turns into water vapor. The latent heat of vaporization at body temperature (37 °C) is . The heat absorbed is approximately equal to the average energy given to a single water molecule (H2O) times the number of water molecules that are vaporized. What is ?

** | 57 | A spherical balloon is made from a material whose mass is 3.00 kg. The thickness of the material is negligible compared to the 1.50-m radius of the balloon. The balloon is filled with helium (He) at a temperature of 305 K and just floats in air, neither rising nor falling. The density of the surrounding air is 1.19 kg/m3. Find the absolute pressure of the helium gas.

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