AP Physics 2 : Work, Enthalpy, and Internal Energy

Example Questions

Example Question #1 : Work, Enthalpy, And Internal Energy

In the cylinder of a certain internal combustion engine, the hot gas caused by the combustion of the fuel expands from  to a volume of  at a constant pressure of . How much work will the gas do on the piston during this expansion?

Explanation:

Work is defined as pressure times change in volume for constant pressure cases. Work done on the gas takes a positive sign in the AP equation sheet, and the equation for work is given with a negative sign. This question asks for work on the piston, not on the gas (or "system" in AP parlance), and since the force and displacement are in the same direction for the piston, it has positive work done on it, increasing its kinetic energy.

Example Question #2 : Work, Enthalpy, And Internal Energy

Suppose that a sample of an ideal, monatomic gas containing  moles is held inside of a container at a temperature of  Kelvin. What is the internal energy of this sample?

Explanation:

For this question, we're given the amount of gas (in moles) as well as the temperature of the gas (in Kelvin) and we're being asked to determine the internal energy of this gas.

It's important to recall that internal energy is a microscopic (as opposed to macroscopic) measurement of the energy of a system. The internal energy of a system includes the kinetic energy of the individual atoms or molecules, which can be caused by translational motion, vibrational motion, and rotational motion. In addition, the internal energy also includes any potential energy that results from intermolecular interactions between the atoms or molecules.

We're told in the question stem that the gas under consideration is both ideal as well as monatomic. Because it is ideal, we can assume that there is no significant intermolecular interactions between the gas particles, which therefore means that there is no need to worry about the potential energy component of internal energy. Moreover, we're told that the gas under consideration is monatomic, which means that the kinetic energy component of internal energy is only caused by translational motion; in other words, we can neglect vibrational and rotational contributions to kinetic energy.

The significance of all this is that we can relate the internal energy of this gas solely to the translational motion. Thus, we'll need to use an expression that relates the variables given in the question stem.

The above expression tells us that the total internal energy, , of a gas is proportional to the number of moles of gas as well as the absolute temperature of the gas.

If we plug in the quantities given in the question stem, we find our answer.

Example Question #3 : Work, Enthalpy, And Internal Energy

A piston is filled with methane at a pressure of  with a current volume of . If the methane doubles in volume isobarically, how much work does the gas do on the surrounding environment?

Explanation:

Since the problem statement tells us that this is an isobaric process, we can use the following expression:

The statement also tells us that we start with 2L of gas and end up with double that amount, or 4L. Therefore, the change in volume is 2L. Plugging this and our pressure into the above expression, we get:

However, these units are not compatible, so we need to do some unit analysis:

Example Question #4 : Work, Enthalpy, And Internal Energy

of nitrogen is allowed to expand from  to  at a constant temperature of . How much work does the gas do on the surroundings?

Explanation:

Since the problem statement tells us that the gas expands at a constant temperature, we can use the expression for isothermal expansion:

We have all of these values, so it's just important that we choose the correct gas constant. Since we are working with joules and Kelvin, we will use:

Plugging in values for each variable:

Example Question #5 : Work, Enthalpy, And Internal Energy

How much heat does it take to bring  of ethanol from  to a saturated vapor?

Use the following values for ethanol in your calculations:

Explanation:

There are two calculations that we will need to perform to calculate the total energy needed. The first is the energy needed to bring the ethanol to its boiling point. Then, the energy needed to bring the ethanol to its saturated vapor state, which simply means that all of the ethanol has vaporized but is still at it's boiling point temperature. So, we will first calculate how much energy is needed to bring the ethanol to its boiling point:

Now we need to calculate the energy it takes to vaporize all of the ethanol:

Now adding these together:

Example Question #5 : Work, Enthalpy, And Internal Energy

A system absorbs heat  and has an equal amount of positive work done on it. What is the change in the internal energy of the system?

(internal energy decreases)

Explanation:

Heat is absorbed so that is a  to internal energy. Also, positive work is done on the system so that is another  to internal energy. The total internal energy is increased by .

Example Question #7 : Work, Enthalpy, And Internal Energy

Determine the energy needed to bring a rigid metal can of volume  from a pressure of  to .

None of these

Explanation:

Energy due to a compressed gas:

Plugging in values:

Converting units:

Example Question #6 : Work, Enthalpy, And Internal Energy

A gas with a fixed number of molecules has  of work done on it, and  of heat are transferred from the gas to the surroundings. What happens to the internal energy of the gas?

It increases by

It does not change

It increases by

It decreases by

It decreases by

It increases by

Explanation:

Since  of work are done on the gas, its internal energy increases by . Then,  of heat are transferred to the surroundings, which decreases the internal energy by . The net result is .

Example Question #4 : Work, Enthalpy, And Internal Energy

A gas has a constant pressure of  as it expands by . What is the net work performed on the gas?

Explanation:

The net work is equal to the pressure times the change in volume. So the pressure is  and the change in volume is . Multiplying the two will equal .

Example Question #7 : Work, Enthalpy, And Internal Energy

If the volume of a balloon is expanded by  against a constant external pressure of , how much heat energy would have to be added in order for the balloon to maintain the same temperature?

Explanation:

We're asked to find the amount of heat energy that must be added to a balloon undergoing expansion against a constant external pressure in order for it to maintain a constant temperature.

The situation being described in the question stem is one of isothermal expansion, meaning that the temperature doesn't change. In other words, we can say that the internal energy of the gas held within the balloon does not change.

Furthermore, we can define the amount of work done by the gas on the balloon as follows.

Combining these expression, we can obtain the following.

Finally, if we plug in the values given to us, we can get our answer.