To determine the new volume of the gas after it heats to a temperature of 30°C in your lungs, you can use the ideal gas law equation, which states:
PV = nRT
Where: P = Pressure of the gas (assuming constant) V = Volume of the gas n = Number of moles of gas (assuming constant) R = Ideal gas constant (assuming constant) T = Temperature of the gas in Kelvin
To solve this problem, you'll need to convert the temperatures from Celsius to Kelvin.
Given: Initial volume (V1) = 3.2 liters Initial temperature (T1) = 16°C = 16 + 273.15 = 289.15 K Final temperature (T2) = 30°C = 30 + 273.15 = 303.15 K
Assuming the pressure and number of moles remain constant, we can set up the following proportion:
V1 / T1 = V2 / T2
Now, plug in the given values:
3.2 / 289.15 = V2 / 303.15
To find V2, cross-multiply and solve for V2:
V2 = (3.2 / 289.15) * 303.15 V2 ≈ 3.33 liters
Therefore, the new volume of the gas after heating to a temperature of 30°C in your lungs is approximately 3.33 liters.