# 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.

**Q2: **

A cylinder with a movable lid contains gas with a volume of
0.022 m^{3}.
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 m^{3}
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 m^{3}
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 m^{3} 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/m^{3}.
Answer to three significant figures.

**Q6: **

A weather balloon has an initial volume of
1.2 m^{3},
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 m^{3},
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
- B
- C
- D
- E

**Q7: **

A cylinder with a movable lid contains air with a volume
of 0.042 m^{3} at 101 kPa pressure. The cylinder lid is pushed downward
by an external force , as shown in
the diagram. The force includes the lidβs 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 cylinderβs 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 m^{3} 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/m^{3} for
the density of water. The water temperature is uniform. Answer to three
significant figures.

**Q10: **

A balloon is inflated by adding more air to it, increasing its volume, as shown in the diagram. The pressure of the air in the balloon is 101 kPa before it is inflated and is 121 kPa after it is inflated. The temperature of the air in the balloon does not change when it is inflated. The air can be assumed to behave as an ideal gas.

Find the volume of the balloon when it is inflated as a percent of the volume of the balloon before it is inflated. Answer to three significant figures.

- A375%
- B63.6%
- C275%
- D19.8%
- E175%

Find the mass of the air in the balloon when it is inflated as a percent of the mass of the balloon before it is inflated. Answer to three significant figures.

- A329%
- B429%
- C130%
- D229%
- E69.6%