Adiabatic process, Poisson equation Lesson plan

Long-term plan unit: Fundamentals of thermodynamics

School:

Date:

Teacher name:

Grade: 10

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Theme of the lesson

Application of the first law of thermodynamics to isoprocesses. Adiabatic process, Poisson equation.

Learning objectives that are achieved at this lesson (Subject Program reference)

·                    apply the first law of thermodynamics to isoprocesses and adiabatic process; 

Lesson objectives

·                    derive the formula TV^γ-1 = constant from the first law of thermodynamics

·                    apply the first law of thermodynamics to isoprocesses and adiabatic process; 

·                    use the equation to solve problems on some practical situations

Assessment        criteria

·                    derive the formula TV^γ-1 = constant from the first law of thermodynamics

·                    apply the first law of thermodynamics to isoprocesses and adiabatic process; 

·                    use the equation to solve problems in some practical situations

Language objectives

- put technical terms into context

- define the terms:

Type of differentiation

Different questions are asked to students differentiating according to their cognitive ability. Gifted students will be expected to answer the advanced questions and challenged students may answer standard level questions.

Values instilled at the lesson

Long Learning, Academic Integrity and Transparency, Respect for Self and Others

Values are implemented through the ethical use of electromagnetic waves by humans.

Cross-curricular links

Mathematics: derivation, integration  and graphical analysis

English: Use of English as the medium of discussion during the lesson

ICT skills  

Interactive Problems at:

https://cnx.org/contents/OFwJyVav@8/Adiabatic-Processes-for-an-Ideal-Gas

Previous learning

Students should be aware about the first law of thermodynamics (∆U = ∆Q - ∆W) and the values of C_p and C_v. Moreover, knowledge of derivatives and integrating quantities are essential in this lesson.

Course of the lesson

Planned stages of the lesson

Planned activities at the lesson

Resources

Beginning

(2 min)

Preliminaries

Setting the mood. Greet students.

“Good morning everyone, please sit down.”

“Do you have questions with your homework?”

Middle

(8 min)

(2 min)

(10 min)

(15 min)

Part I.  Revision by pair

Ask students to fill in the table with the correct information from the concepts shown on the board.

The teacher may say:

“Please fill in the table with the correct required information”

Recall Concepts(3 min)

Recall Isoprocesses (5 min)

Show the slide 2.

The teacher may say:

“We have studied 3 isoprocesses so far; isobaric where pressure is constant (W =  p∆V), isochoric wherein the volume is constant (W = 0), isothermic wherein the temperature is constant ( ∆U = 0).

The fourth of the four thermodynamic processes that we are going to talk about is adiabatic process which is a change of state for a gas and it’s done adiabatically as we call it. In this case, Q = 0. Q stands for the heat that is added or removed from the gas.

Question: Now if we are not adding or removing heat from the gas, how can the gas do work?

Answer: The only way the gas can do work with is from its internal energy. If the gas has to do work, then its internal energy has to go down. As the internal energy goes down, the temperature goes down as well.

Show the PV graph of an adiabatic process.

The teacher may say:

“An adiabatic process may look like this. The yellow lines show the isotherms (constant temperature) and you can see the green line goes from a higher temperature to a lower temperature because it is losing internal energy.”

“An adiabatic process is a very quick process that heat neither escape from the gas or enter the gas, therefore Q is zero.

Therefore, from the equation, ∆U = ∆Q - ∆W; Q = 0, making ∆U = - ∆W

or W = -∆U ; ∆U = nC_V∆T

thus, W = - n C_V ∆T (C_V is the constant volume specific heat)”

The problem with an adiabatic process is that we don’t know what the temperature change is so we have to find a way to relate the temperature to the volume. And so the question is, “How do Temperature and Volume Relate?”

Part II. Problem, Topic and Lesson Objectives (2 min)

Problem: How do T and V relate?

Topic:  Application of the first law of thermodynamics to Isoprocesses. adiabatic process, Poisson equation.

Objectives:

·                    derive the formula TV^γ-1 = constant from the first law of thermodynamics

·                    apply the first law of thermodynamics to isoprocesses and adiabatic process; 

·                    use the equation to solve problems in some practical situations

Part III.  Interactive Lecture  (10 min)

Well, the first to way to relate temperature and volume is to equate W to pressure multiplied to delta V.

W = - n C_V ∆T, but W = pdV

Thus,

pdV = - n C_V dT

We have to write dV and dT in the expression since we are dealing with very small interval of time.

In an adiabatic process, pressure, volume and temperature all change. In the other processes, one of them stayed the same. In isobaric the pressure didn’t change, in isochoric the volume didn’t change, and isothermic the temperature didn’t change, so only 2 out of 3 changed. But in an adiabatic process, all variables change.

The next thing to do is to use the ideal gas equation, pV = nRT,

and p = nRT/V, then you can plug that information from the previous equation.

dV) = - n C_V dT , canceling out n gives you

) = -(C_V)(dT/T), moving to one side

) + (C_V)(dT/T) = 0 then integrate both sides

R ln V + c₁ + C_V lnT + c₂ = 0 where c₁ and c₂  are the integration constants

Combining constants

R ln V + C_V lnT =  c₃ where c₃ is the combined integration constant

but R = C_P - C_V, so

(C_P - C_V)(lnV) +  C_V lnT = c₃ dividing both sides by C_V becomes

Different gases have different ratios of C_P/C_V and so we need to have another variable , γ !

                                     where  

which can be rewritten as

                                      or

                                 dividing ln on both sides gives

Other variations of Poisson’s Equations are:

what is gamma

Gamma, γ, depends on the kind of gas present

For monoatomic gas,  γ =1.7

For diatomic gas,  γ = 1.4.

For triatomic gas,  γ  = 1.3)

Part IV. Worksheet (12 min+3 min marking)

Students will answer a differentiated worksheet.

Worksheets are divided into easy, average and difficult.

Gifted students will be expected to answer the advanced questions and challenged students may answer standard level questions.

Slides 1-2

Slide 3

Slide 4

Slide 5

Slides 6-8

Print-out Word document “Interactive lecture worksheet”

Slide 9

Structured questions

For more questions, visit:

https://cnx.org/contents/OFwJyVav@8/Adiabatic-Processes-for-an-Ideal-Gas

End

(3 min)

Reflection

At the end of the lesson students reflect each student writes on a sticky note:

-              What they have learnt

-              What remained unclear

-              What should they work on

All problems that are not completed will be homework.

Differentiation – how do you plan to give more support? How do you plan to challenge the more able learners?

Assessment – how are you planning to check students’ learning?

Health and safety regulations

Different questions are asked to students differentiating according to their cognitive ability. Gifted students will be expected to answer the advanced questions and challenged students may answer standard level questions.

Oral questioning and feedback.

The teacher will check the quality of answers on the students’ worksheets.

There should be good ventilation in the classroom

The temperature in the classroom should be appropriate for effective learning to take place, around 25°C.

There should be a break between the 2 40 minute lessons in which students are encouraged to engage in physical activity.

Students should be reminded to adhere to all safety rules in the laboratory.

Reflection

Were the lesson objectives/learning objectives realistic? Did all learners achieve the LO?

If not, why?

Did my planned differentiation work well?

Did I stick to timings?

What changes did I make from my plan and why?

Use the space below to reflect on your lesson. Answer the most relevant questions from the box on the left about your lesson. 

Summary evaluation

What two things went really well (consider both teaching and learning)?

1:

2:

What two things would have improved the lesson (consider both teaching and learning)?

1:

2:

What have I learned from this lesson about the class or achievements/difficulties of individuals that will inform my next lesson?