All AP Physics 2 Resources
Example Questions
Example Question #1 : Ideal Gas Law
A balloon is in a room that has a constant pressure of and constant temperature of
. How many moles of air must be put into the balloon for
of work to be done on the balloon?
We know that pressure and temperature are constant. Therefore, we can use the following formula for work:
Write out the ideal gas law:
Rearrange for moles:
Substitute in our expression for work:
Now, plug in values for each variable:
Example Question #1 : Ideal Gas Law
Suppose that a gas originally at standard temperature and pressure undergoes a change in which its pressure is quadrupled while its temperature is cut in half. What change in volume does the gas experience during this process?
Decrease by a factor of 8
Decrease by a factor of 2
The volume of the gas will not change
Increase by a factor of 2
Increase by a factor of 8
Decrease by a factor of 8
To solve this problem, we'll need to use the ideal gas equation:
We are told that the gas undergoes a change in which its pressure quadruples and its temperature halves. Therefore:
and
Furthermore, we can set the ideal gas equation to solve for volume:
and
If we plug in the values from above, we obtain:
Therefore, we can see that the new volume is of its original value.
Example Question #1 : Ideal Gas Law
An ideal gas is kept in a container at
and
. How many moles of the gas are in the container?
There is not enough information to determine the number of moles
Because this is an ideal gas, we can use the Ideal Gas Law to determine its state.
The value for is sometimes tricky to determine, because it has several values depending on the units being used. The two main values for
that are used are:
and
Because we have units in Liters, and we can convert our temperature and pressure to Kelvin and atmospheres respectively, we use the second value of .
First, let's convert our values to usable units.
Because we're trying to find moles of gas, we can rearrange the ideal gas equation to equal moles, and plug in our values.
Therefore, there are of gas in the container.
Example Question #1 : Ideal Gas Law
At , the volume of a gas is
. The temperature of the gas gets raised to
with no change in pressure. What is the new volume of the gas?
There is not enough information to determine the new volume
When the only properties of an ideal gas that are changing are volume and temperature, we use Charles' Law (a derivative of the Ideal Gas Law). Charles' Law is as follows:
We're given all but the new volume, . To find the new volume, we rearrange the equation.
The addition of 273.15 is to convert the Celsius units to Kelvin.
Example Question #41 : Thermodynamics
The pressure of a sample of gas is in a
sealed, flexible container. If the pressure gets raised to
at a constant temperature, what is the new volume?
There is no volume change
Because the only properties of the gas that are changing are the pressure and volume1, we use Boyle's Law, a derivative of the Ideal Gas Law. Boyle's Law states
Since can be in atmospheres, and
can be in Liters, we don't have to convert any units. Instead, we just rearrange the equation to solve for
, and plug in our numbers.
The new volume is .
Example Question #6 : Ideal Gas Law
An airship has a volume of . How many kilograms of hydrogen would fit in it at
and
?
None of these
Use the ideal gas equation:
Convert the volume into liters in order to use our ideal gas constant:
Rearrange the ideal gas equation to solve for , then plug in known values and solve.
Example Question #1 : Ideal Gas Law
Assuming ideal gas behavior, find the density of pure oxygen gas at and
.
None of these
For simplicity, we will assume .
Rearrange the ideal gas equation to solve for volume.
Plug in known values and solve.
Use volume to solve for density.
Example Question #1 : Ideal Gas Law
Assuming ideal gas behavior, determine the volume of of methane gas at
and
.
None of these
Use the ideal gas equation and rearrange, solving for volume.
Find by using the molar mass of methane.
Plug in known values into the rearranged ideal gas equation and solve.
Example Question #9 : Ideal Gas Law
In a room where the temperature is , a football has been inflated to a gauge pressure of
. The football is then taken to the field, where the temperature is
. What will the football's gauge pressure be when its temperature becomes equal to the temperature of the air on the field? Assume the air follows the ideal gas law and that the atmospheric pressure that day was
.
Start by converting to Pascals:
For the atmosphere:
Find the absolute pressure in the football:
Write the ideal gas law for the football in the locker room:
Solve for , the constants that won't change as the air cools:
Write the ideal gas law for the football on the field:
Substitute from before:
Recognize that the volume does not change, so those terms cancel:
Convert from absolute pressure to gauge pressure:
Example Question #1 : Ideal Gas Law
How many moles of nitrogen gas are in a tank with a pressure of
at
?
We will use the ideal gas equation:
Where is the pressure in atm,
is the volume in liters,
is the number of moles of gas,
, and
is the temperature in Kelvin.
Rearrange the equation to solve for moles:
Plug in known values and solve.
All AP Physics 2 Resources
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