Five liters of air at -50.0°C are warmed to 100.0°C. What is the new volume if the pressure remains constant?
To solve this problem, you can use Charles' Law, which states that at constant pressure, the volume of a gas is directly proportional to its temperature.
Charles' Law can be mathematically expressed as:
V1 / T1 = V2 / T2
Where:
V1 = Initial volume
T1 = Initial temperature
V2 = Final volume (what we're trying to find)
T2 = Final temperature
In this case, we have:
V1 = 5 liters (initial volume)
T1 = -50.0°C (initial temperature)
T2 = 100.0°C (final temperature)
To solve for V2, we rearrange the equation:
V2 = (V1 * T2) / T1
Now we can plug in the values:
V2 = (5 liters * 100.0°C) / -50.0°C
Calculating this expression, we get:
V2 = -10 liters
Since volume cannot be negative, the answer can't be -10 liters. Therefore, we made a mistake somewhere.
Upon closer inspection, we realize that we need to convert Celsius to Kelvin for temperature values when using gas laws. The Kelvin scale is an absolute temperature scale that does not have negative values.
Converting -50.0°C to Kelvin:
T1(Kelvin) = -50.0°C + 273.15
Converting 100.0°C to Kelvin:
T2(Kelvin) = 100.0°C + 273.15
Now let's recalculate V2:
V2 = (5 liters * (100.0°C + 273.15)) / (-50.0°C + 273.15)
Simplifying this expression, we get:
V2 ≈ 10.98 liters
Therefore, the new volume, when the pressure remains constant, is approximately 10.98 liters.