### All AP Physics 2 Resources

## Example Questions

### Example Question #1 : Thermodynamics

Calculate the entropy change when 2kg of ice melts.

**Possible Answers:**

**Correct answer:**

Since we know the heat of fusion of water on a per mass basis, we can calculate the heat required to melt 2kg of ice:

Ice melts at a constant temperature of .

Now, use the equation for entropy:

### Example Question #1 : Laws Of Thermodynamics

If the isothermal expansion of a gas inside a container absorbs 25 kJ of heat energy, how much work is done by the gas in this process?

**Possible Answers:**

No work is done

**Correct answer:**

Recall that in an isothermal process, the change in internal energy of the has is 0. Thus, we can make use of the following equation to calculate the work done.

Since the change in internal energy is 0, we can rewrite the equation as:

In other words, in order to maintain a constant internal energy of the system, the gas must do the same amount of work on its surrounding as the amount of energy it absorbs from the surroundings in the form of heat.

### Example Question #3 : Thermodynamics

Which of the following is not one of the laws of thermodynamics?

**Possible Answers:**

Energy can only be converted from one form to another; it cannot be created

If two systems are in each in thermal equilibrium, respectively, with a third system, then they must be in thermal equilibrium with each other

All spontaneous processes must lead to an increase of entropy in the universe

At a temperature of absolute zero, all motion within a system ceases

Energy and mass are interconvertible

**Correct answer:**

Energy and mass are interconvertible

In order to find out which of the answer choices is not one of the laws of thermodynamics, we'll need to consider each one.

The zeroth law of thermodynamics says that if two systems are in each in thermal equilibrium, respectively, with a third system, then they must be in thermal equilibrium with each other.

The first law of thermodynamics says that energy can only be converted from one form to another and cannot be created.

The second law of thermodynamics says that all spontaneous processes must lead to an increase of entropy in the universe.

The third law of thermodynamics says that at a temperature of absolute zero, all motion within a system ceases.

The only other answer choice left states that energy and mass are interconvertible. Although this is a true statement, as is stated by Einstein's famous equation , this is not a thermodynamic law.

### Example Question #1 : Thermodynamics

of an ideal gas is at a pressure of . If of heat is transferred to the gas as it expands at a constant pressure of , what is the change in internal energy of the gas?

**Possible Answers:**

**Correct answer:**

We can use the 1st law of thermodynamics to solve this problem:

We are given the heat applied to the system, so we need to calculate the work done by the system. Since we were told that this is isobaric expansion, we can use the following expression for work:

Substituting this in, we get:

Plugging in values, we get:

### Example Question #1 : Thermodynamics

of an ideal gas expands at a constant temperature of . If of energy is inputted into the system and the net change of internal energy , by what factor does the volume of the gas change?

**Possible Answers:**

**Correct answer:**

We will begin with the 1st law of thermodynamics:

We know that there is no change in internal energy, so we can say:

Also, the problem statement tells us that this is isothermal expansion, we can use the following expression for work:

Plugging this into our expression, we get:

Rearranging for the change in volume, we get:

We have all of these values, so time to plug and chug:

### Example Question #1 : Thermodynamics

In an isothermal process, you are told that heat is being added to the system. Which of the following is not** **true?

**Possible Answers:**

Work is being done by the system.

The pressure of the gas is decreasing.

The average kinetic energy of the particles is remaining constant.

Work is being done on the system.

The gas is expanding.

**Correct answer:**

Work is being done on the system.

In an isothermal process, there are two possibilities: the gas is expanding or the gas is being compressed. If the gas is expanding, the gas is doing work and therefore needs heat in order to remain at constant temperature (which is the definition of an isothermal process). If the gas is compressed, then work is being done on the gas and heat must be emitted in order for the temperature to remain constant. We're told heat is added, so the gas must be expanding. This means the volume is increasing and work is being done by the gas. Therefore, those two choices are not the answer. The pressure must decrease, which can be seen using the formula . Since temperature is constant, if volume goes up, pressure must go down. The average kinetic energy (A.K.A. temperature) will remain constant. Work is not being done on the gas, so that is the correct answer.

Both of these conceptual methods of figuring out if heat must be added or released can be mathematically computed using the formula . is the heat added to the gas, denotes the work done by the gas, and denotes the change in internal energy, which is directly related to temperature.

### Example Question #2 : Thermodynamics

A piston alters the gas held in a sealed chamber. If of heat is added to the system when the piston compresses at a constant force of , what is the change in internal energy of the system?

**Possible Answers:**

**Correct answer:**

Here, we need to use the first law of thermodynamics:

Since the heat is added to the system, the sign is positive. Moreover, the work can be calculated using:

Now, we can simply add these two parts to get the change in internal energy.

### Example Question #1 : Heat Transfer And Thermal Equilibrium

of energy is applied to an aluminum rod of unknown mass. Its temperature goes from to . What is the mass of the rod?

**Possible Answers:**

There is not enough information to determine the rod's mass

**Correct answer:**

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:

### Example Question #1 : Heat Transfer And Thermal Equilibrium

Which of the following best defines the zeroth law of thermodynamics in variable form?

**Possible Answers:**

**Correct answer:**

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:

### Example Question #3 : Heat Transfer And Thermal Equilibrium

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?

**Possible Answers:**

There's not enough information to determine the temperature change

**Correct answer:**

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.