Think about the analogy "full of hot air." If a person were to inhale 2.2 L of gas at a temperature of 18 °C and that air heats to a temperature of 38 °C inside the lungs, what would be the new volume of the gas? Round to the nearest hundredth. Don't forget the units.
The Boyle's Law states that
PV/T = k where k is a constant
so, assuming a constant pressure
V/T does not change
2.2/(291.15) = V/(311.15)
V = 2.35 L
To determine the new volume of the gas, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature, assuming constant pressure.
First, we need to convert the temperatures to Kelvin since Charles's Law requires temperature in Kelvin.
To convert Celsius to Kelvin, we add 273.15:
Initial temperature in Kelvin = 18°C + 273.15 = 291.15 K
Final temperature in Kelvin = 38°C + 273.15 = 311.15 K
Next, we can use the formula:
(V1 / T1) = (V2 / T2)
where V1 is the initial volume, T1 is the initial temperature, V2 is the final volume, and T2 is the final temperature.
Plug in the values we have:
(2.2 L / 291.15 K) = (V2 / 311.15 K)
Now, we can solve for V2:
V2 = (2.2 L / 291.15 K) * 311.15 K
Calculating this, we get:
V2 = 2.3443 L
Rounding to the nearest hundredth, the new volume of the gas would be approximately 2.34 L.