Thermodynamics - AP Physics 2
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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?
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?
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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.
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 energy is applied to an aluminum rod of unknown mass. Its temperature goes from 
to 
. What is the mass of the rod?
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The relevant equation for this problem is called the specific heat capacity equation:
In this equation, 
is the total energy in Joules, 
is the mass in grams, 
is the specific heat of the substance in Joules over grams times Coulombs 
, and 
is the change in temperature in Kelvins or degrees Celsius; which one you use doesn't matter because it's the change you need.
To find the mass of the rod when given the energy, specific heat, and change in temperature, we can rearrange the equation to this:
Now, we can plug in our numbers and solve:
The relevant equation for this problem is called the specific heat capacity equation:
In this equation,
To find the mass of the rod when given the energy, specific heat, and change in temperature, we can rearrange the equation to this:
Now, we can plug in our numbers and solve:
Which of the following best defines the zeroth law of thermodynamics in variable form?
Which of the following best defines the zeroth law of thermodynamics in variable form?
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The zeroth law of thermodynamics states that if an object X is in thermal equilibrium with object Y, and object Y also in thermal equilibrium with object Z, then object X must also be in thermal equilibrium with object Z.
refers to the first law of thermodynamics.
refers to the second law of thermodynamics.
is the enthalpy equation.
refers to entropy.
The best choice is:
The zeroth law of thermodynamics states that if an object X is in thermal equilibrium with object Y, and object Y also in thermal equilibrium with object Z, then object X must also be in thermal equilibrium with object Z.
The best choice is:
You have 
of water in a container above a burner. If 
of energy is put into the container (assume all of it goes into the water), and the specific heat of water is 
, how much did the water's temperature rise?
You have
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The equation for temperature change given applied heat is
.
is the amount of heat energy, 
is the mass, 
is the specific heat, and 
is the change in temperature. In this problem, we're given the energy, the mass, and the specific heat, so we need to solve the equation for 
.
Rearranging to find the change in temperature:
Now, we can plug in our numbers.
Therefore, the water changed by about 
degrees celsius given that amount of energy applied.
The equation for temperature change given applied heat is
Rearranging to find the change in temperature:
Now, we can plug in our numbers.
Therefore, the water changed by about
How much energy does it take to raise 
of water by 
?
How much energy does it take to raise
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The equation that is needed is:
Plug in known values and solve.
The equation that is needed is:
Plug in known values and solve.
You have 
of an unknown metal. If, after adding 
of energy to it, its temperature raises by 
, what is the metal's specific heat?
You have
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To find the specific heat of an unknown material given temperature change, mass, and energy applied, we use the following equation:
Plug in known values and solve.
To find the specific heat of an unknown material given temperature change, mass, and energy applied, we use the following equation:
Plug in known values and solve.
The heat capacity for any given material is defined as the amount of heat that must be added to that material in order to increase its temperature by 
. However, the heat capacity for any given material can be measured under different conditions, such as constant pressure or constant volume.
How would the heat capacity for a material at constant volume differ from the heat capacity for that same material at constant pressure?
The heat capacity for any given material is defined as the amount of heat that must be added to that material in order to increase its temperature by
How would the heat capacity for a material at constant volume differ from the heat capacity for that same material at constant pressure?
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In this question, we're presented with the definition of heat capacity. We're also told that the heat capacity for any given material can be measured at 1) constant volume, or 2) constant pressure. We're being asked to determine whether the constant volume heat capacity is greater than, less than, or equal to the constant pressure heat capacity for the same material.
First, let's revisit the definition of heat capacity. It is the amount of heat that must be added to a material to raise the temperature of that material by 
.
Next, let's consider what is happening as we add heat to a material at constant volume. When the volume of a material is held constant, that means that it is prevented from expanding as heat is added. Thus, all of the heat being added is resulting directly in an increase in the average kinetic energy of the particles that make up that material. In other words, all of the heat being added results in a temperature increase.
Let's now consider what happens when heat is added to a material at constant pressure. In this situation, the material is allowed to expand as heat is added to it (because volume is not being held constant). Therefore, when heat is added to the material, some of the heat will result in an increased temperature, but some of the heat will also result in an expansion of the material. The consequence of this is that in order to increase the temperature of the material by a given amount at constant pressure, it will require more heat energy than at constant volume.
Again, the main point of this is as follows:
- Constant volume - all of the added heat results in increased temperature
- Constant pressure - some of the added heat results in increased temperature and some of the added heat results in expansion
Since only a fraction of the heat being added at constant pressure will actually result in a temperature increase, we'll have to add more heat in order to increase its temperature by a given amount, when compared to constant volume conditions.
In this question, we're presented with the definition of heat capacity. We're also told that the heat capacity for any given material can be measured at 1) constant volume, or 2) constant pressure. We're being asked to determine whether the constant volume heat capacity is greater than, less than, or equal to the constant pressure heat capacity for the same material.
First, let's revisit the definition of heat capacity. It is the amount of heat that must be added to a material to raise the temperature of that material by
Next, let's consider what is happening as we add heat to a material at constant volume. When the volume of a material is held constant, that means that it is prevented from expanding as heat is added. Thus, all of the heat being added is resulting directly in an increase in the average kinetic energy of the particles that make up that material. In other words, all of the heat being added results in a temperature increase.
Let's now consider what happens when heat is added to a material at constant pressure. In this situation, the material is allowed to expand as heat is added to it (because volume is not being held constant). Therefore, when heat is added to the material, some of the heat will result in an increased temperature, but some of the heat will also result in an expansion of the material. The consequence of this is that in order to increase the temperature of the material by a given amount at constant pressure, it will require more heat energy than at constant volume.
Again, the main point of this is as follows:
- Constant volume - all of the added heat results in increased temperature
- Constant pressure - some of the added heat results in increased temperature and some of the added heat results in expansion
Since only a fraction of the heat being added at constant pressure will actually result in a temperature increase, we'll have to add more heat in order to increase its temperature by a given amount, when compared to constant volume conditions.
of ethanol is at a temperature of 
and 
of methanol is at a temperature of 
. If the two gases are in an isolated system together and allowed to transfer heat between each other, at which temperature will they reach thermal equilibrium?
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Since the two gases are in an isolated system, we know that the heat lost by one is equal to the heat gained by the other. Furthermore, we know that the two gases will be in thermal equilibrium when they have the same temperature, which will be some value in between their two initial values. Since methanol is at a higher temperature, we can say that it will loose heat and ethanol will gain that same amount of heat:
Substituting in expressions for each of these, we get:
Where the final temperature is equal for both gases:
Now we simply need to rearrange for the final temperature:
We have all of these values, so time to plug and chug:
Since the two gases are in an isolated system, we know that the heat lost by one is equal to the heat gained by the other. Furthermore, we know that the two gases will be in thermal equilibrium when they have the same temperature, which will be some value in between their two initial values. Since methanol is at a higher temperature, we can say that it will loose heat and ethanol will gain that same amount of heat:
Substituting in expressions for each of these, we get:
Where the final temperature is equal for both gases:
Now we simply need to rearrange for the final temperature:
We have all of these values, so time to plug and chug:
Suppose that a copper bar 
long is raised from a temperature of 
to 
. If the coefficient of thermal expansion for copper is 
, what is the final length of the bar?
Suppose that a copper bar
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To find out how much the bar will change in length, we'll need to use the equation for thermal expansion, which is as follows:
If we plug in the values that we know, we can solve for the change in length of the bar.
Now, we just need to add this value to the original length of the bar, and we will have our final answer.
To find out how much the bar will change in length, we'll need to use the equation for thermal expansion, which is as follows:
If we plug in the values that we know, we can solve for the change in length of the bar.
Now, we just need to add this value to the original length of the bar, and we will have our final answer.
Ana is holding onto an ice cube. Why does it melt in her hand?
Ana is holding onto an ice cube. Why does it melt in her hand?
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According to the second law of thermodynamics, heat flows from hot to cold. Thus, the heat from her hand flows into the ice cube, causing it to melt.
According to the second law of thermodynamics, heat flows from hot to cold. Thus, the heat from her hand flows into the ice cube, causing it to melt.
An ideal heat engine uses the atmosphere as a low temperature reservoir and boiling water as a hot temperature reservoir. Water boils at 
. How much more efficient is the heat engine on a cold day (
) than when it is hot outside (
)?
An ideal heat engine uses the atmosphere as a low temperature reservoir and boiling water as a hot temperature reservoir. Water boils at
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The efficiency of an ideal heat engine is given by:
, where 
and 
stand for hot and cold respectively. To use this equation our temperatures must be in Kelvin. Here is the equation to convert from Celsius to Kelvin.
.
The denominator does not change if the temperature is hot or cold, so we need only consider the numerator. Let's compare both calculations:
Hot Day: 
Cold Day: 
Comparing these two efficiencies, we see that the cold day is roughly 
times as efficient.
The efficiency of an ideal heat engine is given by:
The denominator does not change if the temperature is hot or cold, so we need only consider the numerator. Let's compare both calculations:
Hot Day:
Cold Day:
Comparing these two efficiencies, we see that the cold day is roughly
What happens when an ideal gas is adiabatically compressed?
What happens when an ideal gas is adiabatically compressed?
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Adiabatic means that no heat/energy is transferred. Since the gas is compressed and no heat is transferred, the volume decreases causing the pressure and temperature to rise.
Adiabatic means that no heat/energy is transferred. Since the gas is compressed and no heat is transferred, the volume decreases causing the pressure and temperature to rise.
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?
A balloon is in a room that has a constant pressure of
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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:
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:
An ideal gas is kept in a 
container at 
and 
. How many moles of the gas are in the container?
An ideal gas is kept in a
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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.
Because this is an ideal gas, we can use the Ideal Gas Law to determine its state.
The value for
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
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?
At
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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.
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,
The addition of 273.15 is to convert the Celsius units to Kelvin.
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?
The pressure of a sample of gas is
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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 
.
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
The new volume is
An airship has a volume of 
. How many kilograms of hydrogen would fit in it at 
and 
?
An airship has a volume of
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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.
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
Assuming ideal gas behavior, find the density of pure oxygen gas at 
and 
.
Assuming ideal gas behavior, find the density of pure oxygen gas at
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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.
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.
Assuming ideal gas behavior, determine the volume of 
of methane gas at 
and 
.
Assuming ideal gas behavior, determine the volume of
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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.
Use the ideal gas equation and rearrange, solving for volume.
Find
Plug in known values into the rearranged ideal gas equation and solve.
A balloon filled is filled with pure nitrogen gas. The balloon is determined to have a volume of 
on a day when the temperature is 
, and the air pressure is 
.
How many nitrogen molecules are present?
A balloon filled is filled with pure nitrogen gas. The balloon is determined to have a volume of
How many nitrogen molecules are present?
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We will use our ideal gas equation.
Where 
is the pressure
is the volume
is the number of moles
is the gas constant
is the temperature in Kelvin
We rearrange the equation to solve for n
A common mistake is using the wrong gas constant, 
. We need to use
We convert our temperture from Celsius to Kelvin
We plug in our values
We then need to multiply by Avogadros number to convert to number of molecules.
We will use our ideal gas equation.
Where
We rearrange the equation to solve for n
A common mistake is using the wrong gas constant,
We convert our temperture from Celsius to Kelvin
We plug in our values
We then need to multiply by Avogadros number to convert to number of molecules.