Certainly! Let's consider a scenario involving a gas contained in a rigid, sealed container, such as a metal canister filled with air.
Scenario:
Imagine that the canister is placed in an oven to heat up. Initially, the air inside the canister is at room temperature (20 degrees Celsius) and at atmospheric pressure (approximately 101.3 kPa).
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Initial State:
- Pressure (P1) = 101.3 kPa
- Temperature (T1) = 20 °C (which is 293 K in Kelvin)
- Volume (V) = constant (the volume of the canister that does not change)
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Heated Condition: As the oven temperature rises, the temperature of the air inside the canister also increases. Let's say the oven is set to 180 degrees Celsius.
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Final State:
- At this new temperature (T2 = 180 °C or 453 K), the gas particles inside the canister move more rapidly.
Using the combined gas law, which is stated as (P1 * V) / T1 = (P2 * V) / T2, we see that since the volume (V) is constant, we can simplify the equation to P1 / T1 = P2 / T2.
As the temperature increases, the pressure inside the canister also rises. We can calculate the new pressure:
- Initial Pressure in Kelvin: T1 = 293 K
- Final Temperature in Kelvin: T2 = 453 K
- Using the ratio: P2 = P1 * (T2/T1)
- Calculating Final Pressure: P2 = 101.3 kPa * (453 K / 293 K) = 153.9 kPa
Conclusion:
As the temperature of the gas increases due to heating in the oven, the pressure inside the rigid canister also increases (from 101.3 kPa to approximately 153.9 kPa) while the volume remains constant. This scenario illustrates how temperature and pressure of a gas are directly proportional when volume is held constant, in accordance with the combined gas law.
However, it's important to note that if the pressure were to exceed the canister's design limits, it could potentially lead to dangerous situations such as an explosion. Thus, this demonstrates both the application of the gas law and the importance of safety in handling pressurized gases.