Answer :
Answer:
The total pressure is 58.2 atm
Explanation:
Step 1: Data given
The tire is inflated to a volume of 11.8 L and a gauge pressure of 36.0 psi
Atmospheric pressure is 14.7 psi, at a temperature of 12.0 °C
When the tire warms to 65.0 °C, it's volume expands to 12.2 L
Step 2: Calculate total pressure
Gauge pressure = total pressure – atmospheric pressure
Total pressure = gauge pressure + atmospheric pressure
Total pressure in 11.8 liter volume = 36.0 atm + 14.7 atm = 50.7 atm
Step 3: Calculate pressure after temperature rise
Temperature = 12°C + 273 = 285 K
The tire warms to 65.0 ∘C = 273 + 65 = 338 K
P1V1/T1 = P2V2/T2
50.7 atm*(11.8 liters)/ 285 K = P2(12.2 liters)/338 K
P2 = 50.7(11.8)*(338) / 285*(12.2)
P2 = 58.2 atm
Total pressure = 58.2 atm
Step 4: Calculate gauge pressure
Gauge pressure = 58.2 atm – 14.7 atm = 43.5 atm
The total pressure is 58.2 atm