0. Math Review

1. Intro to Physics Units

2. 1D Motion / Kinematics

3. Vectors

4. 2D Kinematics

5. Projectile Motion

6. Intro to Forces (Dynamics)

7. Friction, Inclines, Systems

8. Centripetal Forces & Gravitation

9. Work & Energy

10. Conservation of Energy

11. Momentum & Impulse

12. Rotational Kinematics

13. Rotational Inertia & Energy

14. Torque & Rotational Dynamics

15. Rotational Equilibrium

16. Angular Momentum

17. Periodic Motion

18. Waves & Sound

19. Fluid Mechanics

20. Heat and Temperature

21. Kinetic Theory of Ideal Gases

22. The First Law of Thermodynamics

23. The Second Law of Thermodynamics

24. Electric Force & Field; Gauss' Law

25. Electric Potential

26. Capacitors & Dielectrics

27. Resistors & DC Circuits

28. Magnetic Fields and Forces

29. Sources of Magnetic Field

30. Induction and Inductance

31. Alternating Current

32. Electromagnetic Waves

33. Geometric Optics

34. Wave Optics

36. Special Relativity

[BOOK PHYS] !CLUTCH

Doubling Pressure & Temperature

At an altitude of 11,000 m (a typical cruising altitude for a jet airliner), the air temperature is -56.5°C and the air density is 0.364 kg/m^3 . What is the pressure of the atmosphere at that altitude? (Note: The temperature at this altitude is not the same as at the surface of the earth, so the calculation of Example 18.4 in Section 18.1 doesn't apply.)

0.00086 moles of an ideal gas undergoes the process shown in the figure. If the initial temperature was <math display="inline"><mrow><mn>340</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">K</mi></mrow></math> and the final pressure is <math display="inline"><mrow><mn>5.0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">atm</mi></mrow></math>, what is the final temperature? 
<img src="https://media.pearsoncmg.com/aw/aw_knight_physics_5/msa/content/practice-test/img/CQ18_11_Figure.jpg" alt="A pressure versus volume graph. A process is represented by a vertical line which extends upward from point at p = 2 atmospheres to some point at a higher pressure. ">

An inflated bicycle inner tube is 2.2 cm in diameter and 200 cm in circumference. A small leak causes the gauge pressure to decrease from 110 psi to 80 psi on a day when the temperature is 20°C. What mass of air is lost? Assume the air is pure nitrogen.

A diver 50 m deep in 10°C fresh water exhales a 1.0-cm-diameter bubble. What is the bubble's diameter just as it reaches the surface of the lake, where the water temperature is 20°C?

3 moles of an ideal gas fill a cubical box with a side length of 30cm. If the temperature of the gas is 20°C, what is the pressure inside the container?

A large cylindrical tank contains 0.750 m^3 of nitrogen gas at 27°C and 7.50 * 10^3 Pa (absolute pressure). The tank has a tight-fitting piston that allows the volume to be changed. What will be the pressure if the volume is decreased to 0.410 m^3 and the temperature is increased to 157°C?

Meteorology. The vapor pressure is the pressure of the vapor phase of a substance when it is in equilibrium with the solid or liquid phase of the substance. The relative humidity is the partial pressure of water vapor in the air divided by the vapor pressure of water at that same temperature, expressed as a percentage. The air is saturated when the humidity is 100%. (a) The vapor pressure of water at 20.0°C is 2.34 * 10^3 Pa. If the air temperature is 20.0°C and the relative humidity is 60%, what is the partial pressure of water vapor in the atmosphere (that is, the pressure due to water vapor alone)?

0.10 mol of argon gas is admitted to an evacuated 50 cm^3 container at 20°C. The gas then undergoes an isochoric heating to a temperature of 300°C.

b. Show the process on a pV diagram. Include a proper scale on both axes.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/d3d287226fb65c89-1683241371994.jpg" alt="" />

A sample of gas is heated in a closed container with a volume of <math display='inline'><mrow><mn>2</mn><mo>.</mo><mrow><mn>2</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">L</mi></mrow><mo>,</mo></mrow></math> from an initial temperature and pressure of <math display='inline'><mrow><mn>20</mn><mo>&#x00B0;</mo><mtext>&#x200B;</mtext><mi mathvariant="normal">C</mi></mrow></math> and <math display='inline'><mrow><mn>1</mn><mo>.</mo><mn>0</mn><mtext>&#x00A0;</mtext><mtext>atm</mtext></mrow></math> to a final temperature of <math display='inline'><mrow><mn>238</mn><mo>&#x00B0;</mo><mtext>&#x200B;</mtext><mi mathvariant="normal">C</mi></mrow></math>. What is the final pressure?

The semiconductor industry manufactures integrated circuits in large vacuum chambers where the pressure is 1.0×10^−10 mm of Hg.

b. At T=20°C, how many molecules are in a cylindrical chamber 40 cm in diameter and 30 cm tall?

A gas at 100°C fills volume V₀. If the pressure is held constant, what is the volume if 

(a) the Celsius temperature is doubled

Modern vacuum pumps make it easy to attain pressures of the order of 10^-13 atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. (a) At a pressure of 
9.00 * 10^-14 atm and an ordinary temperature of 300.0 K, how many molecules are present in a volume of 1.00 cm^3?

A gas with an initial temperature of 900°C undergoes the process shown in FIGURE EX18.35.

c. How many moles of gas are there? <img src="https://lightcat-files.s3.amazonaws.com/problem_images/5aab8ff3c4b28d2b-1683044212160.jpg" alt="" />

A balloon contains 3900cm3 of a gas at a pressure of 101 kPa and a temperature of –9°C. If the balloon is warmed such that the temperature rises to 28°C, what volume will the gas occupy? Assume the pressure remains constant.

An ideal gas is in a sealed container. It has a temperature T when it has volume V at pressure P. What is the temperature of the gas when its volume is quadrupled, and the pressure is halved?

The Ideal Gas Law

Gases: The Ideal Gas Law

Ideal Gas Law

Helium gas with a volume of 3.20 L, under a pressure of 0.180 atm and at 41.0°C, is warmed until both pressure and volume are doubled. (a) What is the final temperature?

10 g of dry ice (solid CO₂) is placed in a 10,000 cm^3 container, then all the air is quickly pumped out and the container sealed. The container is warmed to 0°C, a temperature at which CO₂ is a gas.

a. What is the gas pressure? Give your answer in atm. The gas then undergoes an isothermal compression until the pressure is 3.0 atm, immediately followed by an isobaric compression until the volume is 1000 cm^3.

Five grams of nitrogen gas at an initial pressure of 3.0 atm and at 20°C undergo an isobaric expansion until the volume has tripled.

b. What is the gas temperature after the expansion (in °C)? The gas pressure is then decreased at constant volume until the original temperature is reached.

In Problems 67, 68, 69, and 70 you are given the equation(s) used to solve a problem. For each of these, you are to

b. Draw a pV diagram.

V₂=(400+273) K / (50+273) K×1×200 cm^3

Ideal Gas Problems: Crash Course Chemistry #13

A 20-cm-diameter cylinder that is 40 cm long contains 50 g of oxygen gas at 20°C.

d. What is the reading of a pressure gauge attached to the tank?

5 Ideal Gas Law Experiments  - PV=nRT or PV=NkT

The pressure of a gas at the triple point of water is 1.35 atm. If its volume remains unchanged, what will its pressure be at the temperature at which CO2 solidifies?

Martian Climate. The atmosphere of Mars is mostly CO2 (molar mass 44.0 g/mol) under a pressure of 650 Pa, which we shall assume remains constant. In many places the temperature varies from 0.0°C in summer to -100°C in winter. Over the course of a Martian year, what are the ranges of (b) the density (in mol/m^3) of the atmosphere?

Planetary Atmospheres. (a) Calculate the density of the atmosphere at the surface of Mars (where the pressure is 650 Pa and the temperature is typically 253 K, with a CO2 atmosphere), Venus (with an average temperature of 730 K and pressure of 92 atm, with a CO2 atmosphere), and Saturn's moon Titan (where the pressure is 1.5 atm and the temperature is -178°C, with a N2 atmosphere).

A 20.0-L tank contains 4.86 * 10^-4 kg of helium at 18.0°C. The molar mass of helium is 4.00 g/mol. (a) How many moles of helium are in the tank?

The total lung capacity of a typical adult is 5.0 L. Approximately 20% of the air is oxygen. At sea level and at a body temperature of 37°C, how many oxygen molecules do the lungs contain at the end of a strong inhalation?

Solving Ideal Gas Problems With Changing States

In Problems 67, 68, 69, and 70 you are given the equation(s) used to solve a problem. For each of these, you are to

a. Write a realistic problem for which this is the correct equation(s).

(T₂+273) K=200 kPa / 500 kPa ×1×(400+273) K

Ideal Gas Law Practice Problems & Examples

A 20.0-L tank contains 4.86 * 10^-4 kg of helium at 18.0°C. The molar mass of helium is 4.00 g/mol. (b) What is the pressure in the tank, in pascals and in atmospheres?

Helium gas with a volume of 3.20 L, under a pressure of 0.180 atm and at 41.0°C, is warmed until both pressure and volume are doubled. (b) How many grams of helium are there? The molar mass of helium is 4.00 g/mol.

0.0050 mol of gas undergoes the process 1→2→3 shown in FIGURE EX18.37. What are

(a) temperature T₁, <img src="https://lightcat-files.s3.amazonaws.com/problem_images/9690bb1f55dc07f6-1685983947227.jpg" alt="" />

A gas at 100°C fills volume V₀. If the pressure is held constant, what is the volume if 

(b) the Kelvin temperature is doubled?

The semiconductor industry manufactures integrated circuits in large vacuum chambers where the pressure is 1.0×10^−10 mm of Hg.

a. What fraction is this of atmospheric pressure?

A large organic molecule has a mass of 1.41 * 10^-21 kg. What is the molar mass of this compound?

A gas with initial state variables p₁, V₁ , and T₁ expands isothermally until V₂=2V₁. What are 

and (b) p₂?

In Problems 67, 68, 69, and 70 you are given the equation(s) used to solve a problem. For each of these, you are to

a. Write a realistic problem for which this is the correct equation(s).

p₂=300 cm^3/ 100 cm^3 ×1×2 atm

0.10 mol of argon gas is admitted to an evacuated 50 cm^3 container at 20°C. The gas then undergoes an isochoric heating to a temperature of 300°C.

a. What is the final pressure of the gas?

A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains 0.110 m^3 of air at a pressure of 0.355 atm. The piston is slowly pulled out until the volume of the gas is increased to 0.390 m^3. If the temperature remains constant, what is the final value of the pressure?

A gas with an initial temperature of 900°C undergoes the process shown in FIGURE EX18.35.

a. What type of process is this? <img src="https://lightcat-files.s3.amazonaws.com/problem_images/271f244efc530537-1683037978771.jpg" alt="" />

A 20-cm-diameter cylinder that is 40 cm long contains 50 g of oxygen gas at 20°C.

c. What is the number density of the oxygen?

How many moles are in a 1.00-kg bottle of water? How many molecules? The molar mass of water is 18.0 g/mol

Hydrogen gas behaves very much like an ideal gas. If you have a sample of Hydrogen gas with a volume of 1000 cm3&nbsp;at 30°C with a pressure of 1 × 105 Pa, calculate how many hydrogen atoms (particles) there are in the sample.

How Close Together Are Gas Molecules? Consider an ideal gas at 27°C and 1.00 atm. To get some idea how close these molecules are to each other, on the average, imagine them to be uniformly spaced, with each molecule at the center of a small cube. (a) What is the length of an edge of each cube if adjacent cubes touch but do not overlap?

A container of gas at 2.0 atm pressure and 127°C is compressed at constant temperature until the volume is halved. It is then further compressed at constant pressure until the volume is halved again.

b. Show this process on a pV diagram.

0.0050 mol of gas undergoes the process 1→2→3 shown in FIGURE EX18.37. What are

and (c) volume V₃? <img src="https://lightcat-files.s3.amazonaws.com/problem_images/0f240035b0e9f0f3-1685982280016.jpg" alt="" />

Modern vacuum pumps make it easy to attain pressures of the order of 10^-13 atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. (b) How many molecules would be present at the same temperature but at 1.00 atm instead?

Ideal Gas Law Practice Problems with Molar Mass

A gas with initial state variables p₁, V₁, and T₁ is cooled in an isochoric process until p₂=1/3p₁. What are 

(a) V₂?

If a certain amount of ideal gas occupies a volume V at STP on earth, what would be its volume (in terms of V) on Venus, where the temperature is 1003°C and the pressure is 92 atm?

A 24-cm-diameter vertical cylinder is sealed at the top by a frictionless 20 kg piston. The piston is 84 cm above the bottom when the gas temperature is 303°C. The air above the piston is at 1.00 atm pressure.

b. What will the height of the piston be if the temperature is lowered to 15°C?

0.0050 mol of gas undergoes the process 1→2→3 shown in FIGURE EX18.37. What are

(b) pressure p₂, <img src="https://lightcat-files.s3.amazonaws.com/problem_images/06af0805fb882207-1685983492778.jpg" alt="" />

Ideal Gases and the Ideal Gas Law

A sealed container holds 3.2 g of oxygen at 1 atm pressure and 20°C. The gas first undergoes an isobaric process that doubles the absolute temperature, then an isothermal process that halves the pressure. What is the final volume of the gas in L?

In a gas at standard conditions, what is the length of the side of a cube that contains a number of molecules equal to the population of the earth (about 7 * 10^9 people)?

You have several identical balloons. You experimentally determine that a balloon will break if its volume exceeds 0.900 L. The pressure of the gas inside the balloon equals air pressure (1.00 atm). (a) If the air inside the balloon is at a constant 22.0°C and behaves as an ideal gas, what mass of air can you blow into one of the balloons before it bursts?

A gas with initial state variables p₁, V₁, and T₁ expands isothermally until V₂=2V₁. What are

(a) T₂

Ideal Gas Law Explained

The solar corona is a very hot atmosphere surrounding the visible surface of the sun. X-ray emissions from the corona show that its temperature is about 2×10^6 K. The gas pressure in the corona is about 0.03 Pa. Estimate the number density of particles in the solar corona.

A constant-volume gas thermometer registers an absolute pressure corresponding to 325 mm of mercury when in contact with water at the triple point. What pressure does it read when in contact with water at the normal boiling point?

Five grams of nitrogen gas at an initial pressure of 3.0 atm and at 20°C undergo an isobaric expansion until the volume has tripled.

a. What is the gas volume after the expansion?

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