homeworkA

firstlaw-labA.pdf

Lab: 1st Law of Thermodynamics 1 Physics 242

I. Work A. Recall the definition of work done on an object by an agent that exerts a force on that object. (You may wish to

consult your textbook or notes.) Write out the definition below.

In the spaces provided, sketch

arrows representing (1) a force

exerted on an object and (2)

the displacement of that object

for cases in which the work

done by the agent is:

B. A block is pushed by a hand as it moves from the bottom to the top of a frictionless incline. The block is speeding up at a constant acceleration.

1. In the space provided, draw a free-body diagram for the block. Make sure the label for each force indicates:

• the type of force,

• the object on which the force is exerted, and

• the object exerting the force.

2. In the space provided, draw an arrow to show the direction of the net force on the block. Explain.

3. State whether the following quantities are positive, negative, or zero. In each case, explain your reasoning.

• the work done on the block by the hand

• the work done on the block by the incline

• Note: the work done on the block by the Earth is negative. You can prove this to yourself by breaking up the weight force into components.

4. Is there work done on the hand by the block in this motion? If so, is this work positive, negative, or zero? Explain.

Frictionless incline

Free-body diagram for block

Net force on block

Lab: 1st Law of Thermodynamics 2 Physics 242

C. An ideal gas is contained in a cylinder. The cylinder is closed by a piston as shown in the diagram at right. There is no friction between

the piston and the cylinder walls.

1. Describe the direction of the force that the gas exerts on the piston.

2. Describe the direction of the displacement of the piston: if the volume of the gas in the cylinder is increasing.

if the volume of the gas in the cylinder is decreasing.

3. In each of the two cases in part 2, does the gas do work on the piston?

How could the piston move so that the work the gas does on the piston is:

• positive?

• negative?

How could the piston move so that the work the piston does on the gas is:

• positive?

• negative?

Chemistry texts and physics texts use different conventions when talking about the Work in the statement of the 1st Law. It is therefore important for you to know if the text is discussing the work done by the gas on the piston or the work done by the piston on the gas.

Check your answers with your instructor before you continue.

Lab: 1st Law of Thermodynamics 3 Physics 242

II. Work and internal energy (Process 1)

A. Imagine that the cylinder from section I is thermally isolated from its surroundings by placing it in an insulating jacket. The piston is

pressed inward to the position shown at right. We will refer to this

compression as process 1.

Is the work done on the piston by the gas positive, negative, or zero?

In thermal physics, we are often interested in the internal energy (U) of a system. The internal energy of an

ideal gas is proportional to the temperature and the number of moles of the gas. When a system is thermally

isolated, the change in internal energy of the system is equal to the negative of the work done by the gas on

the piston:

DU = - Wby gas (for a thermally isolated system)

B. 1. Does the internal energy of a gas in an insulated cylinder increase, decrease, or remain the same when the piston is pushed inward? Explain.

2. Does the temperature of the gas change? Explain.

C. A student makes the following statement about process 1:

“The volume of the gas decreases, but the pressure increases. Therefore, by the ideal gas law, the temperature must remain the same.”

Do you agree or disagree with the student? Explain.

Check your reasoning with a tutorial instructor before you continue.

Lab: 1st Law of Thermodynamics 4 Physics 242

III. Heat (Process 2) A. Imagine that the cylinder from section II is no longer thermally insulated, and the piston is locked in place.

The gas is initially at room temperature.

The cylinder is then placed into boiling water and reaches thermal equilibrium with the water. We refer to

this process as process 2.

1. In process 2, do the following quantities increase, decrease, or remain the same? (Hint: Use the ideal gas law.) Explain.

• the temperature of the gas

• the internal energy of the gas

• the volume of the gas

• the pressure of the gas

2. Sketch process 2 on the PV diagram at right.

3. Is there any work done on the piston in process 2? Explain.

The energy transfer that takes place in this process is called heat transfer. In this process, if the heat

transferred to the gas (Q) is greater than zero, the internal energy of the gas will increase.

B. In process 2, is the heat transfer to the gas positive, negative, or zero? Explain.

C. In process 2, is the heat transfer to the boiling water positive, negative, or zero? Explain.

Lab: 1st Law of Thermodynamics 5 Physics 242

IV. Heat, work, and internal energy

The first law of thermodynamics states that the change in internal energy of a closed system is equal to:

DU = Q - W by gas

A. Explain how you could write this law in terms of the work done by the piston on the gas. How does your textbook express the first law of thermodynamics?

B. In process 1 you did not need to consider heat transfer. What feature of the experiment prevented heat transfer to the gas?

C. In process 2 you did not need to consider work. What feature of the experiment prevented work from being done on the gas?

Check your reasoning with your instructor before you continue.

V. Temperature and internal energy (Process 3)

The cylinder, with the piston still locked in place, is now immersed in a mixture of ice and water and allowed to

come to thermal equilibrium with the mixture. The piston is then moved inward very slowly, in such a way that

the gas is always in thermal equilibrium with the ice-water mixture. We will refer to this slow compression of

the gas as process 3.

A. In process 3, do the following quantities increase, decrease, or remain the same? Explain.

• the volume of the gas

• the temperature of the gas

• the internal energy of the gas

• the pressure of the gas

Lab: 1st Law of Thermodynamics 6 Physics 242

B. Sketch process 3 on the PV diagram provided.

C. Determine whether the following quantities are positive, negative, or zero:

• the work done on the piston in process 3 (Explain your reasoning by referring to a force and a displacement.)

• the heat transfer to the gas in process 3

D. Are your answers above consistent with the first law of thermodynamics? Explain.

E. How does the compression in process 3 differ from the compression in process 1? Explain.

F. A student is considering process 3:

“The temperature doesn’t change; it is an isothermal process. Therefore, the heat transfer must be zero.”

Do you agree with this student? Explain.