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Charles' Law
Charles' Law
[MELC 21] Investigate the relationship between: 1. volume and pressure at a constant temperature of a gas. 2. volume and temperature at a constant pressure of gas; and 3. explain these relationships using the kinetic molecular theory. (S9MT-IIj-20)
Day 6: Plot data and infer the volume-temperature relationship at the constant pressure of a gas.
Day 7: Cite examples/situations where Charles’ Law is observed.
Day 8: Calculate for each unknown on volume and temperature relationship at a constant pressure of a gas.
Jacques Charles, a French physicist who lived from 1746 to 1823, studied the effect of temperature on the volume of a gas at constant pressure. This led to the formulation of Charles's Law, which states that the volume of a given mass of gas varies directly with its absolute temperature when the pressure is kept constant. The Kelvin scale is used to measure absolute temperature because zero on this scale corresponds to a complete stoppage of molecular motion [©].
The table below showcases data on temperature and volume for a specific gas sample at constant pressure. This data exemplifies Charles' Law, which states that the volume of a gas directly correlates with its Kelvin temperature at constant pressure[©].
Examples/situations where Charles’ Law is observed
Inflated objects and temperature
As the temperature increases, the gas molecules inside an inflated object move faster and hit the walls of the container more frequently. This increased pressure can cause the object to expand. Conversely, when the temperature decreases, the gas molecules move slower and the object may contract.
Hot air balloons
Hot air balloons work because heated air expands. When air inside the balloon is heated, it becomes less dense than the cooler surrounding air. This difference in density creates buoyancy, allowing the balloon to rise.
Breathing
As we inhale, air enters our lungs and expands due to the increased temperature inside the body compared to the outside environment. When we exhale, the air cools and contracts as it exits the lungs.
The mathematical relationship between volume and temperature is: V1/T1 =V2/T2
Where
V1 is the starting volume
T1 is the starting temperature
V2 is the final volume and
T2 is the final temperature.
Example Problem 1
A bicycle tire contains 2.0 liters of air at a temperature of 20°C (293 K). If the bicycle is left outside on a hot day where the temperature reaches 35°C (308 K), what will the new volume of the air in the tire be, assuming the pressure stays constant?
Given:
V1 = 2.0 L
T1 = 293 K
T2 = 308 K
Required
V2
Equation
V1/T1 =V2/T2
Rearranged to V2 = V1 * T2 / T1
Solution
V2 = 2.0 L * 308 K / 293 K
Answer
V2 = 2.08 L
Example Problem 2
A sealed steel canister containing a fixed amount of gas has a volume of 4.0 L at sea level (approximately 1 atm pressure). The canister is then transported to a high mountain peak where the pressure remains relatively constant (ignoring minor pressure changes). Due to the colder environment, the gas contracts to a final volume of 3.2 L. What was the final temperature (T2) at the mountain peak, if the initial temperature at sea level was 25°C (298 K)?
Given:
V1 = 4.0 L
V2 = 3.2 L
T1 = 298 K
Required
T2
Equation
V1/T1 =V2/T2
Rearranged to T2 = V2 * T1 / V1
Solution
T2 = 3.2 L * 298 K / 4.0 L
Answer
T2 ≈ 238.4 K
The final temperature (T2) at the mountain peak would be approximately 238.4 K.
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