GCSE Physics Tutorial - Calculating the Change in Pressure of a Gas Volume (with Fixed Mass and Temperature) When Volume or Pressure is Increased or Decreased
In this tutorial, we will learn how to calculate the change in pressure of a gas volume when either the volume or pressure is increased or decreased, while keeping the mass and temperature constant. Understanding these calculations is crucial in analysing gas behaviour under different conditions and in practical applications. We will use Boyle's Law, which describes the relationship between pressure and volume for a fixed mass of gas at constant temperature. Let's dive into the world of gas pressure, volume, and the associated calculations!
Boyle's Law: Boyle's Law states that for a fixed mass of gas at constant temperature, the product of the pressure (p) and volume (V) remains constant. In mathematical terms, this is represented as pV = constant.
Calculation When Volume Changes: When the volume of a gas changes from an initial value (V₁) to a final value (V₂) while keeping the mass and temperature constant, we can calculate the change in pressure (Δp) using the pressure-volume equation:
p₁V₁ = p₂V₂
Rearranging the equation to calculate Δp: Δp = p₂ - p₁
Calculation When Pressure Changes: Similarly, when the pressure of a gas changes from an initial value (p₁) to a final value (p₂) while keeping the mass and temperature constant, we can calculate the change in pressure (Δp) using the pressure-volume equation:
p₁V₁ = p₂V₂
Rearranging the equation to calculate Δp: Δp = p₂ - p₁
Sample Questions: Let's practice calculating the change in pressure for different scenarios:
Question 1: A gas with a fixed mass is initially at a pressure of 200 kPa and a volume of 0.5 m³. If the volume is decreased to 0.3 m³ while keeping the temperature constant, what is the change in pressure?
Solution: Using Boyle's Law, we can calculate the final pressure (p₂) when the volume changes: p₁V₁ = p₂V₂ 200 kPa × 0.5 m³ = p₂ × 0.3 m³ p₂ = (200 kPa × 0.5 m³) / 0.3 m³ p₂ ≈ 333.33 kPa
Now, we can calculate the change in pressure (Δp):
Δp = p₂ - p₁
Δp = 333.33 kPa - 200 kPa
Δp ≈ 133.33 kPa
Answer: The change in pressure is approximately 133.33 kPa.
Question 2: A gas with a fixed mass is initially at a pressure of 150 kPa and a volume of 0.2 m³. If the pressure is increased to 200 kPa while keeping the temperature constant, what is the change in pressure?
Solution: Using Boyle's Law, we can calculate the final volume (V₂) when the pressure changes:
p₁V₁ = p₂V₂
150 kPa × 0.2 m³ = 200 kPa × V₂
V₂ = (150 kPa × 0.2 m³) / 200 kPa
V₂ = 0.15 m³
Now, we can calculate the change in pressure (Δp):
Δp = p₂ - p₁
Δp = 200 kPa - 150 kPa
Δp = 50 kPa
Answer: The change in pressure is 50 kPa.
In this tutorial, we have learned how to calculate the change in pressure of a gas volume when either the volume or pressure is increased or decreased, while keeping the mass and temperature constant. Using Boyle's Law and the pressure-volume equation, we can analyse gas behaviour under different conditions and apply these calculations in practical situations. Keep practicing to further enhance your understanding of gas properties and their relationships with pressure and volume.
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