You were at a gas station in Seattle, where the air temperature was a warm and m

Question

You were at a gas station in Seattle, where the air temperature was a warm and muggy 26.7°C. You'd just finished filling your tires to the specified gauge pressure of 253.25 kPa when you and your car were kidnapped by ninja eskimos and put on a ferryboat to Alaska. You recheck the tire pressure when you get to Alaska and find that the gauge now reads 202.6 kPa even though they didn't lose any air.

(a) What was the initial and final absolute pressure inside your tires, assuming standard atmospheric pressure? (b) What is the air temperature in Alaska, assuming that the volume of the tire tubes is essentially the same? °C

Explanation / Answer

T1 = temp. at Seattle = 26.7 deg C; Pg1 = guage press. of tyres at Seattle = 253.25 x 10 3 Pa

Pg2= guage pressure of tyres at Alaska = 202.6 x 10 3 Pa ; P atmospheric of air = 101325 Pa (atmospheric pressure at

solution a ) guage pressure = absolute pressure - atmospheric pressure

At Seattle : Pg1= P abs seattle - P atm

P abs seattle = P g 1 + P atm = 253.25 x 10 3 + 101.325 x 10 3 = 354.575 KPa

Similarly P abs Alaska = P g 2 + P atm = 202.6 x 10 3 + 101.325 x 10 3 = 303.925 KPa

Hence, P = 303.925 KPa

solution b ) Pabsseattle/ T1 = P abs Alaska/ T2

354.575 / 299.7 = 303.925 / T2

T2= 256.89 K

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