600.0 mL of air is at 20.0 c what is the volume at 60.0
The Correct Answer and Explanation is :
To determine the volume of air at a different temperature, we can use Charles’s Law, which states that the volume of a gas is directly proportional to its absolute temperature (measured in Kelvin) when pressure is held constant. The formula for Charles’s Law is:
[
\frac{V_1}{T_1} = \frac{V_2}{T_2}
]
Where:
- ( V_1 ) is the initial volume
- ( T_1 ) is the initial absolute temperature (in Kelvin)
- ( V_2 ) is the final volume
- ( T_2 ) is the final absolute temperature (in Kelvin)
Given Values:
- Initial volume ( V_1 = 600.0 \, \text{mL} )
- Initial temperature ( T_1 = 20.0 \, \text{°C} )
- Final temperature ( T_2 = 60.0 \, \text{°C} )
Converting Celsius to Kelvin:
To convert Celsius to Kelvin, add 273.15:
- ( T_1 = 20.0 + 273.15 = 293.15 \, \text{K} )
- ( T_2 = 60.0 + 273.15 = 333.15 \, \text{K} )
Applying Charles’s Law:
Now, substituting the values into Charles’s Law:
[
\frac{600.0 \, \text{mL}}{293.15 \, \text{K}} = \frac{V_2}{333.15 \, \text{K}}
]
To find ( V_2 ), we rearrange the equation:
[
V_2 = \frac{600.0 \, \text{mL} \times 333.15 \, \text{K}}{293.15 \, \text{K}}
]
Calculating ( V_2 ):
[
V_2 \approx \frac{600.0 \times 333.15}{293.15} \approx 681.3 \, \text{mL}
]
Conclusion:
The volume of air at 60.0 °C will be approximately 681.3 mL.
Explanation:
This calculation illustrates the fundamental principle that gases expand when heated. As the temperature increases, the kinetic energy of the gas molecules increases, leading to more vigorous motion and a greater volume. The relationship between volume and temperature is linear in this context, emphasizing the direct proportionality of these two variables when pressure is constant. Understanding this relationship is crucial in various applications, including meteorology, engineering, and everyday scenarios like hot air balloons and internal combustion engines.