University Physics Volume 2
18th Edition
ISBN: 9781938168161
Author: OpenStax
Publisher: OpenStax
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Chapter 2, Problem 18P
The gauge pressure in your car tires is
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A deep-sea diver should breathe a gas mixture that has the same oxygen partial pressure as at sea level, where dry air contains 20.9% oxygen and has a total pressure of 1.01 X 105 N/m2. (a) What is the partial pressure of oxygen at sea level? (b) If the diver breathes a gas mixture at a pressure of 2.00 X 106 N/m2, what percent oxygen should it be to have the same oxygen partial pressure as at sea level?
b. After leaving a vehicle in an indoor car park for a night, you check the tyres’ statistics from the dashboard and gotten the value as follows:
Temperature of the air: 24°C
Volume of air: 0.0165 m^3
Absolute pressure of the tyre: 3.01 atm
Current atmospheric pressure: 1.02 atm
To confirm the value, you measure the pressure of the tyre with a gauge pressure and got the value of 1.99 atm. You then drive the car up to Genting Highland where the atmospheric pressure is 0.947 atm due to higher altitude. Once you have reached the destination, the temperature of the air in the tires has now risen to 42.0°C and the volume has risen to 0.0172 m^3. Assume ideal gas in the tyre, calculate the gauge pressure at Genting Highland.
The highest building in Montreal is the ‘1 square building’, with a height of 203m.
The atmospheric pressure in the streets of Montreal is P1 = 9.9 x 104 Pa.
Suppose air density is constant : ρair = 1,2 kg/m3 and g = 9.8 m/s2.
a. Find the pressure difference between the streets and the rooftop of the '1 square building'
b. Find the pressure on the rooftop.
Suppose the rooftop temperature to be T = 298K, and the air composition is 100% N2 molecules.
*c. Find the root-mean-square speed (vrms ).
*d. How would you find the probability for a molecule picked randomly to have a speed in the range vrms and vrms+5.0 m/s. (No calculations needed)
*e. Find the ratio between the most probable speed (vmp) and the mean speed (vmean).
The collision cross-section of N2 molecules is 0.43 nm2.
*f. Find the collision frequency. Is it in the order of magnitude that you were expecting?
Now, consider Earth's atmosphere as 80% N2 and 20% O2. (No calculations needed)
*g.…
Chapter 2 Solutions
University Physics Volume 2
Ch. 2 - Check Your Understanding The recommended daily...Ch. 2 - Check Understanding The density of in a Classroom...Ch. 2 - Check Your Understanding Liquids and solids have...Ch. 2 - Check Your Understanding If you consider a very...Ch. 2 - Check Your Understanding Which has a longer mean...Ch. 2 - Check Your Understanding Suppose 2 moles of helium...Ch. 2 - Two H2 molecules can react with one O2 molecule to...Ch. 2 - Under what circumstances would you expect a gas to...Ch. 2 - A constant-volume gas thermometer contains a fixed...Ch. 2 - Inflate a balloon at room temperature. Leave the...
Ch. 2 - In the last chapter, free convection was explained...Ch. 2 - How is momentum related to the pressure exerted by...Ch. 2 - If one kind of molecule has double the radius of...Ch. 2 - What is the average velocity of the air molecules...Ch. 2 - Why do the atmospheres of Jupiter, Saturn, Uranus,...Ch. 2 - Statistical mechanics says that in a gas...Ch. 2 - Which is more dangerous, a closet where tanks of...Ch. 2 - Experimentally it appears that many polyatomic...Ch. 2 - One might think that the internal energy of...Ch. 2 - You mix 5 moles of H2 at 300 K with 5 moles of He...Ch. 2 - One cylinder contains helium gas and another...Ch. 2 - Repeat the previous question if one gas is still...Ch. 2 - An ideal gas is at a temperature of 300 K. To...Ch. 2 - The gauge pressure in your car tires is...Ch. 2 - Suppose a gas-filled incandescent light bulb is...Ch. 2 - People buying food in sealed bags at high...Ch. 2 - How many moles are there in (a) 0.0500 g of N2 gas...Ch. 2 - A cubic container of volume 2.00 L holds 0.500 mol...Ch. 2 - Calculate the number of moles in the 2.00-L volume...Ch. 2 - An airplane passenger has 100 cm3 of air in his...Ch. 2 - A company advertises that it delivers helium at a...Ch. 2 - According to...Ch. 2 - An expensive vacuum system can achieve a pressure...Ch. 2 - The number density N/V of gas molecules at a...Ch. 2 - A bicycle tire contains 2.00 L of gas at an...Ch. 2 - In a common demonstration, a bottle is heated and...Ch. 2 - A high-pressure gas cylinder contains 50.0 L of...Ch. 2 - Find the number of moles in 2.00 L of gas at 35.0 ...Ch. 2 - Calculate the depth to which Avogadro's number of...Ch. 2 - (a) What is the gauge pressure in a 25.0 cc car...Ch. 2 - A person hits a tennis ball with a mass of 0.058...Ch. 2 - A person is in a closed room (a racquetball court)...Ch. 2 - Five bicyclists are riding at the following...Ch. 2 - Some incandescent light bulbs are filled with...Ch. 2 - Typical molecular speeds (vrms) are large, even at...Ch. 2 - What is the average kinetic energy in joules of...Ch. 2 - What is the ratio of the average translational...Ch. 2 - What is the total translational kinetic energy of...Ch. 2 - The product of the pressure and volume of a sample...Ch. 2 - What is the gauge pressure inside a tank of...Ch. 2 - If the rms speed of oxygen molecules inside a...Ch. 2 - The escape velocity of any object from Earth is...Ch. 2 - The escape velocity from the Moon is much smaller...Ch. 2 - Nuclear fusion, the energy solute of Sun, hydrogen...Ch. 2 - Suppose that the typical speed (vrms) of carbon...Ch. 2 - (a) Hydrogen molecules (molar mass is equal to...Ch. 2 - There are two important isotopes of uranium, U235...Ch. 2 - The partial pressure of carbon dioxide in the...Ch. 2 - Dry air consists of approximately 78% nitrogen,...Ch. 2 - (a) Using data from the previous problem, find the...Ch. 2 - (a) Given that air is 21% oxygen, find the minimum...Ch. 2 - (a) If the partial pressure of water vapor is 8.05...Ch. 2 - To give a helium atom nonzero angular momentum...Ch. 2 - (a) How much heat must be added to raise the...Ch. 2 - A sealed, rigid container of 0.560 mol of an...Ch. 2 - A sample of neon gas (Ne, molar mass M=20.2 g/mol)...Ch. 2 - A steel container of mass 135 g contains 24.0 g of...Ch. 2 - A sealed room has a volume of 24 m3. It's filled...Ch. 2 - Heliox, a mixture of helium and oxygen, is...Ch. 2 - Professional divas sometimes use heliox,...Ch. 2 - In car racing, one advantage of mixing liquid...Ch. 2 - In a sample of hydrogen sulfide ( M=34.1 g/mol) at...Ch. 2 - Using the approximation v1v1+v f(v)dvf(v1)v for...Ch. 2 - Using the method of the preceding problem,...Ch. 2 - By counting squares in the following figure,...Ch. 2 - Using a numerical integration method such as...Ch. 2 - Find (a) the most probable speed, (b) the average...Ch. 2 - Repeat the preceding problem for nitrogen...Ch. 2 - At what temperature is the average speed of carbon...Ch. 2 - The most probable speed for molecules of a gas at...Ch. 2 - a) At what temperature do oxygen molecules have...Ch. 2 - In the deep space between galaxies, the density of...Ch. 2 - (a) Find the density in SI units of air at a...Ch. 2 - The air inside a hot-air balloon has a temperature...Ch. 2 - When an air bubble rises from the bottom to the...Ch. 2 - (a) Use the ideal gas equation to estimate the...Ch. 2 - One process for decaffeinating coffee uses carbon...Ch. 2 - On a winter day when the air temperature is 0 ,...Ch. 2 - On a warm day when the air temperature is 30 , a...Ch. 2 - (a) People often think of humid air as "heavy."...Ch. 2 - The mean flee path for helium at a certain...Ch. 2 - The mean free path for methane at a temperature of...Ch. 2 - In the chapter on fluid mechanics, Bernoulli's...Ch. 2 - Find the total number of collisions between...Ch. 2 - (a) Estimate the specific heat capacity of sodium...Ch. 2 - A sealed, perfectly insulated container contains...Ch. 2 - Find the ratio f(vp)/f(vrms) for hydrogen gas (...Ch. 2 - Unreasonable results. (a) Find the temperature of...Ch. 2 - Unreasonable results. (a) Find the sped of...Ch. 2 - An airtight dispenser for drinking water is 25 cm...Ch. 2 - Eight bumper cars, each with a mass of 322 kg. are...Ch. 2 - Verify that vp=2kBTm.`Ch. 2 - Verify the normalization equation 0f(v)dv=1 In...Ch. 2 - Verify that v=8kBTm. Make the same scaling...Ch. 2 - Verify that vrms=v2=3kBTm.`
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- A vertical cylinder of cross-sectional area A is fitted with a tight-fitting, frictionless piston of mass m (Fig. P18.40). The piston is not restricted in its motion in any way and is supported by the gas at pressure P below it. Atmospheric pressure is P0. We wish to find the height h in Figure P18.40. (a) What analysis model is appropriate to describe the piston? (b) Write an appropriate force equation for the piston from this analysis model in terms of P, P0, m, A, and g. (c) Suppose n moles of an ideal gas are in the cylinder at a temperature of T. Substitute for P in your answer to part (b) to find the height h of the piston above the bottom of the cylinder. Figure P18.40arrow_forwardReview. (a) Derive an expression for the buoyant force on a spherical balloon, submerged in water, as a function of the depth h below the surface, the volume Vi of the balloon at the surface, the pressure P0 at the surface, and the density w of the water. Assume the water temperature does not change with depth, (b) Does the bouyant force increase or decrease as the balloon is submerged? (c) At what depth is the buoyant force one-half the surface value?arrow_forwardA cylinder with a piston holds 0.50 m3 of oxygen at an absolute pressure of 4.0 atm. The piston is pulled outward, increasing the volume of the gas until the pressure drops to 1.0 atm. If the temperature stays constant, what new volume does the gas occupy? (a) 1.0 m3 (b) 1.5 m3 (c) 2.0 m3 (d) 0.12 m3 (e) 2.5 m3arrow_forward
- (a) An ideal gas occupies a volume of 1.0 cm3 at 20.C and atmospheric pressure. Determine the number of molecules of gas in the container, (b) If the pressure of the 1.0-cm3 volume is reduced to 1.0 1011 Pa (an extremely good vacuum) while the temperature remains constant, how many moles of gas remain in the container?arrow_forwardHow many cubic meters of helium are required to lift a light balloon with a 400-kg payload to a height of 8 000 m? Take Hc = 0.179 kg/m3. Assume the balloon maintains a constant volume and the density of air decreases with the altitude z according to the expression pair = 0e-z/8 000, where z is in meters and 0 = 1.20 kg/m3 is the density of air at sea level.arrow_forwardAt what temperature is the average speed of carbon dioxide molecules ( M=44.0 g/mol) 510 m/s?arrow_forward
- (a) An ideal gas occupies a volume of 1.0 cm3 at 20.C and atmospheric pressure. Determine the number of molecules of gas in the container, (b) If the pressure of the 1.0-cm3 volume is reduced to 1.0 1011 Pa (an extremely good vacuum) while the temperature remains constant, how many moles of gas remain in the container?arrow_forwardA cylinder that has a 40.0-cm radius and is 50.0 cm deep is filled with air at 20.0C and 1.00 atm (Fig. P10.74a). A 20.0-kg piston is now lowered into the cylinder, compressing the air trapped inside as it takes equilibrium height hi (Fig. P16.74b). Finally, a 25.0-kg dog stands on the piston, further compressing the air, which remains at 20C (Fig. P16.74c). (a) How far down (h) does the piston move when the dog steps onto it? (b) To what temperature should the gas be warmed to raise the piston and dog back to hi?arrow_forwardA vertical cylinder of cross-sectional area A is fitted with a tight-fitting, frictionless piston of mass m (Fig. P16.56). The piston is not restricted in its motion in any way and is supported by the gas at pressure P below it. Atmospheric pressure is P0. We wish to find die height h in Figure P16.56. (a) What analysis model is appropriate to describe the piston? (b) Write an appropriate force equation for the piston from this analysis model in terms of P, P0, m, A, and g. (c) Suppose n moles of an ideal gas are in the cylinder at a temperature of T. Substitute for P in your answer to part (b) to find the height h of the piston above the bottom of the cylinder.arrow_forward
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