The tire is inflated (while cold) to a volume of 11.8 l and a gauge pressure of 36.0 psi (note: the gauge pressure is the difference between the total pressure and atmospheric pressure. in this case, assume that atmospheric pressure is 14.7 psi.) at a temperature of 12.0 ∘c. while driving on a hot day, the tire warms to 65.0 ∘c and its volume expands to 12.2 l. what is the total pressure (gauge pressure + atmospheric pressure) in the tire after warming on a hot day?

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

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