Question

The absolute pressure of an automobile tire is measured to be 320 kPa before a trip and 349 kPa after the trip. Assuming the volume of the tire remains constant at 0.022 m^3, determine the percent increase in the absolute temperature of the air in the tire. The percent increase in the absolute temperature of the air in the tire is_____ %.

Answer 1

9%

Step-by-step explanation:

An ideal gas is one that has its molecules widely dispersed and does not interact with each other, studies have shown that air behaves like an ideal gas, so the state change equation for ideal gases can be applied.

P1V1T2 = P2V2T1

where 1 corresponds to state 1 = 320kPa

and 2 is state 2 = 349kPa.

Given that the volume remains constant the equation is:

P1T2=P2T1

SOLVING for T2/T1

`(T2)/(T1) =(P2)/(P1) =(349)/(320) =1.09\\\\`

The equation to calculate the percentage increase is as follows

%ΔT=
`((T2-T1)100)/(T1) =((T2)/(T1) -1)100=(1.09-1)100=(0.09)100=9%`