the recommended pressure for a certain truck tire is 1.72X10^5 Pascals above atm

Question

the recommended pressure for a certain truck tire is 1.72X10^5 Pascals above atmospheric pressure. the temperature of the day the tire is filled is 20 degrees C and the air pressure is 9.836X10^4 Pascals.

a) what is the intial pressure of this tire after being inflated?

b) what will the pressure of this tire be when the tire temperature is 50 degree C assuming no change in atmospheric pressure (assume no air added to the tire).

Please help. Having trouble figuring out. Please show me steps

Thanks

Explanation / Answer

a. Since recomended Pressure is 1.72X10^5 Pa above atomspheric Pressure (9.836X10^4 Pa)

Initial pressure afterinflation = Patm+ Precomended= 9.836X10^4 Pa + 1.72X10^5 Pa = 2.7036 * 10 ^5 Pa

b. Since the volume of tyre is constant. As temperature Increases, Pressure Increases. Assuming air to be ideal gas P1/T1=P2/T2 .

Here temperature should be taken in Kelvin

Pfinal/(50+273) = Pintial/(273+20)

Therefore

Final Pressure = 2.98 * 10^5 Pascals

Thanks and all the best .

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