General Gas Law Calculations for SS 3

Class: SS 3
Term: First Term
Week: 3
Age: 16 years
Duration: 45 minutes
Subject: Refrigeration and Air Conditioning
Topic: Temperature and pressure
Subject Matter: Calculations involving general gas law formulae p1v1 = p2v2; T1 T2; PV = MRT
Previous Lesson: Maintenance Tests

Specific Objectives

By the end of the lesson, pupils/students should be able to:

Cognitive Domain

• State the formulas for the Combined Gas Law and the Ideal Gas Law.
• Identify the variables and their standard units in both gas law formulas.
• Explain the importance of converting temperature to Kelvin in gas law calculations.

Affective Domain

• Appreciate the practical application of gas laws in refrigeration and air conditioning.
• Demonstrate patience and accuracy when performing complex calculations.

Psychomotor Domain

• Solve numerical problems using the Combined Gas Law formula.
• Solve numerical problems using the Ideal Gas Law formula.
• Accurately convert temperature units for gas law calculations.

Social Domain

• Collaborate with peers to solve gas law problems.

Reference Materials

The following resources were used in planning this lesson:

• 2025 Revised 9 Years Basic Education Curriculum
• Relevant State Unified Scheme of Work
• Refrigeration and Air Conditioning textbook for SS 3
• The HeadTeacher Scheme of work

Instructional Materials

The teacher will teach this lesson with the aid of:

• Whiteboard or blackboard
• Markers or chalk
• Calculators
• Textbooks
• Charts showing gas law formulas

Rationale for the Lesson

Understanding and applying gas law calculations is fundamental in Refrigeration and Air Conditioning. These calculations enable technicians to predict system behavior, troubleshoot issues, and design efficient cooling and heating systems. Mastery of these formulas ensures accurate system analysis and safe operation.

Prerequisite/Previous Knowledge

Students should have a basic understanding of pressure, volume, and temperature, as well as an introduction to Boyle’s Law, Charles’s Law, and Gay-Lussac’s Law. They should also be familiar with basic algebraic manipulation and unit conversions.

Lesson Content/Board Summary

Temperature and Pressure: General Gas Law Calculations

Combined Gas Law

The Combined Gas Law combines Boyle’s Law, Charles’s Law, and Gay-Lussac’s Law. It describes the relationship between pressure, volume, and temperature of a fixed amount of gas.

Formula

(frac{P_1V_1}{T_1} = frac{P_2V_2}{T_2})

Where:

1. (P_1) = Initial pressure (e.g., Pascals (Pa), atmospheres (atm), psi)
2. (V_1) = Initial volume (e.g., cubic meters (m³), litres (L))
3. (T_1) = Initial absolute temperature (Kelvin, K)
4. (P_2) = Final pressure (e.g., Pascals (Pa), atmospheres (atm), psi)
5. (V_2) = Final volume (e.g., cubic meters (m³), litres (L))
6. (T_2) = Final absolute temperature (Kelvin, K)

Note: Temperature must always be in Kelvin (K). To convert Celsius to Kelvin, use the formula: (T_K = T_C + 273.15).

Example 1

Question: A gas occupies 10 L at 27°C and 1 atm pressure. What will be its volume at 127°C and 2 atm pressure?

Solution:

Step 1: Convert temperatures to Kelvin.

(T_1 = 27°C + 273.15 = 300.15 K)

(T_2 = 127°C + 273.15 = 400.15 K)

Step 2: Write the formula and identify given values.

(frac{P_1V_1}{T_1} = frac{P_2V_2}{T_2})

(P_1 = 1 text{ atm}, V_1 = 10 text{ L}, T_1 = 300.15 text{ K})

(P_2 = 2 text{ atm}, V_2 = ?, T_2 = 400.15 text{ K})

Step 3: Rearrange the formula to solve for (V_2).

(V_2 = frac{P_1V_1T_2}{P_2T_1})

Step 4: Substitute the values.

(V_2 = frac{(1 text{ atm})(10 text{ L})(400.15 text{ K})}{(2 text{ atm})(300.15 text{ K})})

Step 5: Simplify and write the answer.

(V_2 = frac{4001.5}{600.3} approx 6.666 text{ L})

Answer: (6.67 text{ L})

Example 2

Question: A refrigerant gas has a volume of 0.5 m³ at 200 kPa and 0°C. If its volume changes to 0.3 m³ and temperature rises to 50°C, what is the new pressure?

Solution:

Step 1: Convert temperatures to Kelvin.

(T_1 = 0°C + 273.15 = 273.15 K)

(T_2 = 50°C + 273.15 = 323.15 K)

Step 2: Write the formula and identify given values.

(frac{P_1V_1}{T_1} = frac{P_2V_2}{T_2})

(P_1 = 200 text{ kPa}, V_1 = 0.5 text{ m}^3, T_1 = 273.15 text{ K})

(P_2 = ?, V_2 = 0.3 text{ m}^3, T_2 = 323.15 text{ K})

Step 3: Rearrange the formula to solve for (P_2).

(P_2 = frac{P_1V_1T_2}{V_2T_1})

Step 4: Substitute the values.

(P_2 = frac{(200 text{ kPa})(0.5 text{ m}^3)(323.15 text{ K})}{(0.3 text{ m}^3)(273.15 text{ K})})

Step 5: Simplify and write the answer.

(P_2 = frac{32315}{81.945} approx 394.35 text{ kPa})

Answer: (394.35 text{ kPa})

Ideal Gas Law (PV = mRT)

The Ideal Gas Law relates the pressure, volume, temperature, and mass of a gas, incorporating the specific gas constant.

Formula

(PV = mRT)

Where:

1. (P) = Absolute pressure (Pascals, Pa)
2. (V) = Volume (cubic meters, m³)
3. (m) = Mass of the gas (kilograms, kg)
4. (R) = Specific gas constant (Joules per kilogram-Kelvin, J/(kg·K))
5. (T) = Absolute temperature (Kelvin, K)

Note: (R) is specific to each gas. For air, (R approx 287 text{ J/(kg·K)}). Pressure must be in Pascals (1 kPa = 1000 Pa).

Example 1

Question: Calculate the mass of 2 m³ of air at 200 kPa and 27°C. (Assume (R_{text{air}} = 287 text{ J/(kg·K)})).

Solution:

Step 1: Convert pressure to Pascals and temperature to Kelvin.

(P = 200 text{ kPa} = 200 times 1000 = 200000 text{ Pa})

(T = 27°C + 273.15 = 300.15 text{ K})

Step 2: Write the formula and identify given values.

(PV = mRT)

(P = 200000 text{ Pa}, V = 2 text{ m}^3, R = 287 text{ J/(kg·K)}, T = 300.15 text{ K})

Step 3: Rearrange the formula to solve for (m).

(m = frac{PV}{RT})

Step 4: Substitute the values.

(m = frac{(200000 text{ Pa})(2 text{ m}^3)}{(287 text{ J/(kg·K)})(300.15 text{ K})})

Step 5: Simplify and write the answer.

(m = frac{400000}{86143.05} approx 4.643 text{ kg})

Answer: (4.64 text{ kg})

Example 2

Question: A cylinder contains 0.5 kg of oxygen at 100 kPa and 20°C. What is the volume of the cylinder? (Assume (R_{text{oxygen}} = 259.8 text{ J/(kg·K)})).

Solution:

Step 1: Convert pressure to Pascals and temperature to Kelvin.

(P = 100 text{ kPa} = 100 times 1000 = 100000 text{ Pa})

(T = 20°C + 273.15 = 293.15 text{ K})

Step 2: Write the formula and identify given values.

(PV = mRT)

(P = 100000 text{ Pa}, m = 0.5 text{ kg}, R = 259.8 text{ J/(kg·K)}, T = 293.15 text{ K})

Step 3: Rearrange the formula to solve for (V).

(V = frac{mRT}{P})

Step 4: Substitute the values.

(V = frac{(0.5 text{ kg})(259.8 text{ J/(kg·K)})(293.15 text{ K})}{100000 text{ Pa}})

Step 5: Simplify and write the answer.

(V = frac{38089.41}{100000} approx 0.3809 text{ m}^3)

Answer: (0.381 text{ m}^3)

Teaching Methods/Instructional Techniques

Explanation, Demonstration, Guided Practice, Problem Solving, Question and Answer, Individual Practice

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Review/Engage

Teacher’s Activity: The teacher briefly reviews the individual gas laws (Boyle’s, Charles’, Gay-Lussac’s) and asks students about their combined effect on gas behaviour. The teacher then introduces the lesson topic: calculations involving the General Gas Law and Ideal Gas Law.

Pupils’ Activity: Pupils recall previous knowledge of individual gas laws and listen attentively to the introduction of the new topic.

Learning Point: Gas law review

Step 2: Introduction to Combined Gas Law

Time: 8 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher explains the Combined Gas Law, its formula (frac{P_1V_1}{T_1} = frac{P_2V_2}{T_2}), and the meaning of each variable. Emphasizes the importance of using Kelvin for temperature and consistency in units. The teacher then demonstrates Example 1 for the Combined Gas Law on the board, explaining each step clearly.

Pupils’ Activity: Pupils listen, observe the demonstration, and ask questions for clarification. They note down the formula and variable definitions.

Learning Point: Combined Gas Law formula

Step 3: Guided Practice (Combined Gas Law)

Time: 7 minutes

Teaching Skill: Guided Practice

Teacher’s Activity: The teacher guides students through Example 2 for the Combined Gas Law. The teacher asks students to identify the given values, convert units, rearrange the formula, and perform calculations, providing support and correcting errors as they work.

Pupils’ Activity: Pupils actively participate in solving Example 2, converting units, and performing calculations with teacher guidance.

Learning Point: Combined Gas Law application

Step 4: Introduction to Ideal Gas Law (PV = mRT)

Time: 8 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher introduces the Ideal Gas Law formula (PV = mRT), explaining each variable (P, V, m, R, T) and their standard SI units (P in Pa, V in m³, m in kg, R in J/(kg·K), T in K). The teacher highlights the specific gas constant ‘R’ and demonstrates Example 1 for the Ideal Gas Law on the board.

Pupils’ Activity: Pupils listen, observe the demonstration, and note down the Ideal Gas Law formula, variables, and units.

Learning Point: Ideal Gas Law formula

Step 5: Guided Practice (Ideal Gas Law)

Time: 7 minutes

Teaching Skill: Guided Practice

Teacher’s Activity: The teacher guides students through Example 2 for the Ideal Gas Law. The teacher prompts students to convert units, identify variables, rearrange the formula, and calculate the unknown, offering assistance as needed.

Pupils’ Activity: Pupils work through Example 2, converting units, applying the formula, and solving the problem under the teacher’s guidance.

Learning Point: Ideal Gas Law application

Step 6: Independent Practice

Time: 3 minutes

Teaching Skill: Individual Practice

Teacher’s Activity: The teacher provides a simple, short problem from the textbook or a prepared question for students to solve independently, reinforcing the concepts learned.

Pupils’ Activity: Pupils attempt to solve the given problem individually.

Learning Point: Independent problem-solving

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. State the formula for the Combined Gas Law.
2. What unit must temperature always be in for gas law calculations?
3. State the formula for the Ideal Gas Law.
4. What does ‘R’ represent in the Ideal Gas Law?

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Gas law formula recall

Step 8: Note-Taking

Time: 4 minutes

Teaching Skill: Guided Writing

Teacher’s Activity: The teacher guides pupils/students to copy the essential Board Summary notes, including the formulas and worked examples, into their notebooks.

Pupils’ Activity: Pupils/students copy the notes carefully into their notebooks.

Learning Point: Gas law notes recording

Step 9: Conclusion

Time: 2 minutes

Teaching Skill: Consolidation

Teacher’s Activity: The teacher summarises the importance of gas law calculations in Refrigeration and Air Conditioning and encourages students to practice more problems for mastery.

Pupils’ Activity: Pupils listen to the summary and prepare for the next lesson.

Learning Point: Gas law importance

Continuous Assessment/Further Study

Type: Homework

Instruction: Solve the following problems in your notebook:

1. A balloon contains 5 L of air at 25°C and 1.2 atm. If the temperature is increased to 50°C and the pressure remains constant, what is the new volume of the balloon?
2. A tank contains 1.5 kg of nitrogen gas at 250 kPa and 30°C. Calculate the volume of the tank. (Assume (R_{text{nitrogen}} = 296.8 text{ J/(kg·K)})).
3. A gas sample has a volume of 300 mL at 100 kPa and -10°C. What will be its pressure if the volume is reduced to 200 mL and the temperature is raised to 30°C?

Lesson Keywords

• Combined Gas Law – Relates pressure, volume, and temperature of a fixed amount of gas.
• Ideal Gas Law – Relates pressure, volume, temperature, and mass of a gas.
• Pressure (P) – Force per unit area exerted by a gas.
• Volume (V) – Space occupied by a gas.
• Temperature (T) – Measure of the average kinetic energy of gas particles, always in Kelvin for gas laws.
• Mass (m) – Quantity of matter in a gas.
• Specific Gas Constant (R) – A constant unique to each gas in the Ideal Gas Law.
• Kelvin (K) – Absolute temperature scale used in gas law calculations.

Differentiation

For weaker learners, provide additional practice problems with step-by-step guidance and simpler numbers. For faster learners, introduce more complex problems involving multiple unit conversions or ask them to research the derivation of the gas laws or their application in specific refrigeration cycles.

Suggested Lesson Videos

Search on YouTube for: “Combined Gas Law calculations SS3”, “Ideal Gas Law PV=mRT examples refrigeration”

Teacher Guide for Using This Lesson Plan

Before the lesson, ensure you have a clear understanding of both the Combined Gas Law and the Ideal Gas Law formulas, their variables, and common units. Prepare the worked examples on a separate sheet to ensure accuracy and smooth presentation during the demonstration. Emphasize the critical step of converting Celsius temperatures to Kelvin for all gas law calculations. During the guided practice, walk around the classroom to observe students’ progress, identify common errors (e.g., incorrect unit conversions, algebraic mistakes), and provide immediate feedback. Students should copy the Board Summary notes after the main teaching points and before the conclusion to consolidate their learning. Encourage the use of calculators and ensure students understand how to correctly input values and interpret results. Remind students that consistent units are key to accurate answers.