Worksheet: Bulk Properties of an Ideal Gas

In this worksheet, we will practice calculating the relationship between the changes in the pressure, volume, and temperature of an ideal gas.

Q1:

Which of the following formulas most correctly represents the relation between the pressure, volume, and absolute temperature of an ideal gas?

  • A 𝑃 𝑇 ∝ 𝑉
  • B 𝑃 𝑉 ∝ 𝑇
  • C 𝑉 𝑃 ∝ 𝑇
  • D 𝑉 𝑇 ∝ 𝑃
  • E 𝑃 𝑉 ∝ 𝑇

Q2:

A cylinder with a movable lid contains gas with a volume of 0.022 m3. The gas has an initial temperature of 348 K. The temperature is increased to 512 K and the lid rises to equalize the pressure to the value it had before heating. What volume does the gas in the cylinder occupy after it is heated? Answer to three significant figures.

Q3:

A gas cylinder holds 3.25 m3 of gas at a pressure of 520 kPa and a temperature of 300 K. At what temperature would the gas pressure in the cylinder become 865 kPa? Answer to three significant figures.

Q4:

A cloud has a volume of 3,560 m3 when in air with a pressure of 106 kPa and a temperature of 290 K. The air temperature then drops to 275 K and the air pressure drops to 101 kPa, causing the cloud to compress, as shown in the diagram. What is the new volume of the cloud? Answer to the nearest cubic meter.

Q5:

A balloon has a volume of 0.015 m3 at sea level, where the air pressure is 101 kPa and the temperature is 300 K. Find the volume of this balloon at a point 1.4 km above Earth, where the temperature is 245 K. Model the atmosphere as having a uniform density of 1.225 kg/m3. Answer to three significant figures.

  • A 0.110 m3
  • B 0.0220 m3
  • C 0.0147 m3
  • D 0.0736 m3
  • E 0.0125 m3

Q6:

A weather balloon has an initial volume of 1.2 m3, an initial pressure of 102 kPa, and an initial temperature of 290 K. When high in the air, the balloon has a volume of 1.0 m3, a pressure of 96 kPa, and a temperature of 240 K. What percentage of the gas in the balloon has leaked out? Answer to three significant figures.

  • A 3 6 . 5 %
  • B 5 . 2 3 %
  • C 1 . 3 6 %
  • D 3 0 . 4 %
  • E 9 4 . 8 %

Q7:

A cylinder with a movable lid contains air with a volume of 0.042 m3 at 101 kPa pressure. The cylinder lid is pushed downward by an external force F , as shown in the diagram. The force includes the lid’s weight. As a result, the lid moves downward by 10 cm and the air pressure increases by 28 kPa. The lid then stops moving as the pressure above it and below it equalize. The pressure changes linearly as the lid is moved and the temperature of the air does not change during the compression.

What is the area of the cylinder lid? Answer to three significant figures.

What is the cylinder’s height? Answer to three significant figures.

What was the magnitude of the force applied to the lid? Answer to three significant figures.

How much work was done to compress the gas? Answer to three significant figures.

Q8:

A balloon holds 0.012 m3 of air at a pressure of 101 kPa and a temperature of 300 K. The air from this balloon is transferred to another balloon that is half the volume of the first one. 125 kPa of external pressure is required to transfer the air. What is the air temperature in the new balloon? Answer to three significant figures.

Q9:

A rising air bubble in a column of water has a volume at the base of the column and a greater volume near the top of the column, as shown in the diagram. Find the height of the bubble above the base of the column when it has a volume 1.55 times greater than that at the base of the column. Use a value of 101 kPa for atmospheric pressure and a value of 1,000 kg/m3 for the density of water. The water temperature is uniform. Answer to three significant figures.

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