What you absolutely have to know aboutThermodynamics to pass the AP Physic B test!

How to find Work on a pV diagram using

Movement to the right is negative work: An expanding gas moves the environment thus transferring energy from itself to the environment.

Movement to the left is positive work: A gas compressed by an outside force receives energy from the outside environment as a consequence.

What happens when you move up or down on the pV diagram?

Calculus & pV diagrams… (Area under the curve.)

Chris Bruhn Page 1 4/18/2023cbruhn@dallasisd.org(972) 749-2314

What you absolutely have to know aboutThermodynamics to pass the AP Physic B test!

How to find Heat (Q) from a pV diagram using

How do we find Heat (Q) from a pV diagram? Well… we don’t. Not directly anyway. You may have been taught these equations: and in Chemistry or Physics. However, you are not required to know them for the AP Physics B exam. Besides, these two equations are only good for constant pressure and constant volume processes anyway. So, how do we find Heat (Q)? We use the 1st law of Thermo

Here is the procedure:1. We either find W and U from the pV diagram or they are given values in a problem.2. We plug these values into and calculate Q.That’s it!

Here is a practice problem. For each path in the diagram below determine if the value is positive, negative, or zero and fill in the table with a +, -, or 0. (The key is on the last page.)

Path T U W QABCD

How to determine the sign

T is found by seeing how the path moves through the Isotherms.

T & U always have the same sign.

Move to the right = -Move to the left = +

Up or down = 0

Find U and W first.Then use the 1st Law of Thermo to calculate Q.

Chris Bruhn Page 2 4/18/2023cbruhn@dallasisd.org(972) 749-2314

What you absolutely have to know aboutThermodynamics to pass the AP Physic B test!

Round and round we go - Cycles

A cycle is a path on a pV diagram that starts and ends at the same spot. Here are some cycles. Note that each cycle starts at point A and ends at point A. Also, cycle #1 is sometimes referred to as cycle ABCDA.

Lets apply what we have learned: Temp depends on the pV location. Since we start and end at the same spot

Since U & T are related… When ,

That meansU drops out of the 1st Law of Thermo and the equation becomes !

Now look at cycle #1: is negative, &

are both zero, and is positive. Note that the

positive work of is larger than the negative

work of . Thus the net work of cycle #1 is positive! Remember that work = the area under the graph. Look at cycle #1 again. The area under path CD is more than the area under the path AB. Note that the positive and negative areas under the cycle cancel out leaving only the area inside the cycle.

The net work of a cycle = the area inside the cycle. Counterclockwise cycles have a net +W and –Q.Clockwise cycles have a net –W and +Q. Note that we can not find the value of the net work for cycle #3 because of its odd shape. (We would need calculus to find the area of cycle #3.)

Chris Bruhn Page 3 4/18/2023cbruhn@dallasisd.org(972) 749-2314

This area under the cycle cancels out!

The net work of a cycle is simply the

area inside the cycle!

What you absolutely have to know aboutThermodynamics to pass the AP Physic B test!

4 Special Processes (paths) on a pV diagram(When you learn to spot these on a pV diagram your life & AP grade get much better!)

Constant Pressure – Isobaric is easy to calculate since p = constant. These processes more right & left on a pV diagram

Constant Volume – Isochoric / Isovolumetric because thus . These processes move up & down on a pV diagram.

Constant Temperature – Isothermal therefore and . These processes move along the hyperbolic constant pV lines.

No Heat transfer between the system and the environment – Adiabatic thus . This is a curved path similar to an Isothermal but steeper.

What do they look like on the pV diagram? (Note that each of the processes shown below could move in the opposite direction! They just happen to be drawn moving to the right and downward for the problem below.)

Fill in the table below with a +, -, or 0 for each of the 4 special processes as shown above. (Key on last page.)

Path T U W Q#1#2#3#4

How to determine the sign

T is found by seeing how the path moves through the Isotherms.

T & U always have the same sign.

Move to the right = -Move to the left = +

Up or down = 0

Find U and W first. Then use the 1st Law of Thermo to calculate Q.

Chris Bruhn Page 4 4/18/2023cbruhn@dallasisd.org(972) 749-2314