JSS 3: CHARLES'S LAW

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Charles's Law states that the volume of a given mass of gas is directly proportional to its absolute temperature, provided the pressure remains constant.
V ∝ T (V is directly proportional to T)
V/T = k

where: V = Volume
             T = Temperature 
             k = a constant value for a given      
                  sample of gas at a constant 
                   pressure 

V₁/T₁ = k and V₂/T₂ = k, we can set them equal to each other. This gives us the most practical form of Charles's Law:
                         V₁/T₁ = V₂/T₂
Where:
V₁ = Initial volume
T₁ = Initial temperature (in Kelvin)
V₂ = Final volume
T₂ = Final temperature (in Kelvin)
Note: Temperatures must always be converted to Kelvin (K) because the law is based on absolute temperature.
Conversion Formula: K = °C + 273
                  Graph of Charles's Law

Explanation
1. As the temperature of a gas increases, its volume also increases.
2. As the temperature decreases, the volume decreases.
3. Pressure must remain constant throughout the process.

Illustration:
A balloon becomes larger when placed in the sun because the air inside expands. When placed in a refrigerator, the balloon shrinks because the air contracts.

Applications of Charles's Law
1. Hot air balloons rise when the air inside is heated.
2. Vehicle tyres expand on hot days.
3. Bread and cakes rise during baking.
4. Gas-filled balloons shrink in cold weather.

Worked examples 
1. A gas occupies 300 cm³ at 27°C. What will be its volume at 127°C if the pressure remains constant?
Solution
V₁ = 300 cm³
T₁ = 27 + 273 = 300 K
T₂ = 127 + 273 = 400 K
V₂ = ?
V₁/T₁ = V₂/T₂
300/300 =V₂/400
V₂ = 400 cm³

2. A gas occupies 250 cm³ at 20°C. Find its volume at 80°C if the pressure remains constant.
Solution
V₁ = 250 cm³
T₁ = 20 + 273 = 293 K
T₂ = 80 + 273 = 353 K
V₂ = ?
V₁/T₁ = V₂/T₂
250/293 = V₂/353
V₂=____cm³

Class activities 
1. When the temperature of a gas increases at constant pressure, its volume will: (a) Decrease (b) Remain constant (c) Increase (d) Become zero

2. Charles's Law states that the volume of a fixed mass of gas is directly proportional to its: (a) Pressure (b) Density (c) Absolute temperature (d) Mass

3. According to Charles's Law, the pressure of the gas is kept:
(a) Increasing (b) Decreasing (c) Constant (d) Changing

4. If the temperature of a gas is reduced at constant pressure, the volume will:
(a) Increase (b) Decrease (c) Remain unchanged (d) Double

5. The temperature used in Charles's Law calculations must be expressed in:
(a) Celsius (b) Fahrenheit (c) Kelvin (d) Rankine

6. Which of the following best illustrates Charles's Law?
(a) A balloon expands when heated (b) Ice melts into water (c) Sugar dissolves in water (d) Iron rusts in air

7. The mathematical expression for Charles's Law is:
(a) P₁V₁ = P₂V₂ (b) V₁/T₁ = V₂/T₂ (c) PV = nRT (d) P₁/T₁ = P₂/T₂

8. When using Charles's Law, temperatures in degrees Celsius should first be:
(a) Multiplied by 273 (b) Divided by 273 (c) Converted to Kelvin (d) Converted to Fahrenheit

9. Charles's Law applies only when the ________ remains constant.
(a) Pressure (b) Volume (c) Mass (d) Density

10. A gas occupies 200 cm³ at 300 K. If the temperature is increased to 600 K at constant pressure, the new volume will be:
(a) 100 cm³ (b) 200 cm³ (c) 300 cm³ (d) 400 cm³

Assignment
 A gas occupies 500 cm³ at 30°C. Calculate its volume at 150°C if the pressure remains constant.



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