 Gas Laws: Pressure, Volume, and Temperature

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Problems

1. Write the Ideal Gas Law and briefly define its terms.
2. What is the minimum size of a pressure tank to keep the pressure of 4.0 pounds of methane (molecular weight 16) below 800 psig on a hot day with a temperature of 105°F? (Hint: Be careful of units.)
3. At a constant temperature, if the pressure of an ideal gas increases, does the volume for a given amount of material increase or decrease?
4. At a constant volume and amount, if the temperature of an ideal gas increases, does the pressure increase or decrease?
5. What is the compressibility factor z and why is it used?
6. Gas equations of state such as the Ideal Gas Law use (choose a or b)

1. absolute temperature scales such as degrees Rankine or degrees Kelvin.
2. relative temperature scales such as degrees Fahrenheit or degrees Celsius.
7. True or false: For an ideal gas at a constant pressure and temperature, the mole fraction of a component is the same as the volumetric fraction.
8. True or false: “Standard conditions” for gases have been defined by several organizations and are identical in their conditions, although values for temperature and pressure are expressed in different units of measure.
9. According to Boyle’s Law, the volume of a fixed amount of gas at a constant temperature is proportional to pressure by which expression (a or b)?

1. 2. Vp
10. Is the pressure in Boyle’s Law absolute or gauge?
11. According to Charles’s Law, the volume of a fixed amount of gas at a constant pressure is proportional to the temperature by which expression (a or b)?

1. 2. VT
12. Which of the following temperature scales can be used for Charles’s Law: Celsius, Fahrenheit, Kelvin, and/or Rankine?

Given the following data, calculate the volume, V, for exercises 13 through 20:

1. P = 125 psia

T = 600°R

n = 1.2 lb mol

2. P = 75 psia

T = 700°R

n = 3.2 lb mol

3. P = 200 psia

T = 800°R

n = 2.3 lb mol

4. P = 65 psia

T = 650°R

n = 3.8 lb mol

5. P = 200 psig

T = 400°F

n = 4.1 lb mol

6. P = 925 psig

T = 760°F

n = 1.7 lb mol

7. P = 330 psig

T = 1100°F

n = 4.5 lb mol

8. P = 500 psig

T = 1300°F

n = 2.6 lb mol

For exercises 21 through 24, calculate the pressure, P:

1. V = 41 cu.ft.

T = 800°R

n = 3.7 lb mol

2. V = 32.0 cu.ft.

T = 1100°R

n = 4.1 lb mol

3. V = 220 cu.ft.

T = 300°R

n = 2.2 lb mol

4. V = 52 cu.ft.

T = 1200°F

n = 1.7 lb mol

Given the following, calculate the number of lb mols, n, for exercises 25 through 32:

1. P = 250 psia

V = 17 cu.ft.

T = 125°F

2. P = 150 psia

V = 215 cu.ft.

T = 60°F

3. P = 75 psia

V = 29 cu.ft.

T = –40°F

4. P = 200 psia

V = 120 cu.ft.

T = 100°F

5. P = 200 psig

V = 120 cu.ft.

T = 100°F

6. P = 100 psig

V = 220 cu.ft.

T = –150°F

7. P = 60 psig

V = 20 cu.ft.

T = 400°F

8. P = 300 psig

V = 330 cu.ft.

T = 215°F

9. What would the volume of an ideal gas at 250 psig in a pressure tank of 5 cu.ft. be at 1 atmosphere, assuming no change in temperature?
10. What would the pressure of that ideal gas in problem 33 be if the pressure tank was heated from 80°F to 800°F, assuming no release of the gas?
11. After calculating the new pressure of the gas in the cylinder in problem 34, would the increased temperature be needed to calculate the volume of the gas if it were released to the surroundings at 1 atmosphere, assuming no change in temperature when the gas is released?
12. A 5-gallon tank for propane with a molecular mass of 44.0 weighs 17.0 pounds empty and 36.5 pounds full. What is the volume of the propane if it were a gas at 60°F and 14.7 psia?
13. How many pounds of helium with a mole mass of 4.0 lb/lb mol under 2,265 psig at 78°F are there in a number-44 high-pressure steel cylinder that has a volume of 44 liters?
14. What volume of air in cubic feet would the helium in problem 37 displace if it were released in Denver with an atmospheric pressure of 25 in Hg?
15. A 1-gallon steel can is heated to 280°F to boil out all of its liquid contents. If it were sealed immediately after removing it from the heat, what internal pressure would result as it cools to 90°F, assuming that the initial pressure was 14.7 psia?
16. If the 1-gallon can in problem 39 collapsed when it cooled, what minimum volume would it have?
17. What are the two factors that cause gases to behave in a nonideal fashion?
18. Does the nonideal behavior of a gas vary? If so, describe the effect of temperature and the effect of pressure on that variation.
19. Why is it necessary to use “standard” conditions when specifying the rating of gas-processing equipment?
20. Are standard conditions the same in different industries throughout the world?
21. Which of the four sets of standard conditions are equivalent in terms of temperature and pressure?
22. Why is the volume per unit mole irrelevant when specifying the standard condition of temperature and pressure to measure the flow rate of a gas through process equipment such as a compressor?