During a southern Alberta Chinook, 1.06 L of air in a tractor tire at -21°C and 101 kPa is warmed to 35°C and undergoes a pressure decrease to 50kPa. Calculate the final volume of the air.
First, we need to determine the initial volume of the air using the ideal gas law equation:
P1V1/T1 = P2V2/T2
Where:
P1 = initial pressure = 101 kPa
V1 = initial volume = 1.06 L
T1 = initial temperature = -21°C + 273.15 = 252.15 K
P2 = final pressure = 50 kPa
V2 = final volume (unknown)
T2 = final temperature = 35°C + 273.15 = 308.15 K
Now we can plug in the values and solve for V2:
101 kPa * 1.06 L / 252.15 K = 50 kPa * V2 / 308.15 K
V2 = (101 kPa * 1.06 L * 308.15 K) / (252.15 K * 50 kPa)
V2 = 1.32 L
Therefore, the final volume of the air in the tractor tire is 1.32 L.