Ariel’s car tires need air, but it’s a cold morning and she knows the tire pressure will change as the day warms. If it’s 14 ◦C outside now,

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Ariel’s car tires need air, but it’s a cold morning and she knows the tire pressure will change as the day warms. If it’s 14 ◦C outside now, with an expected high of 20 ◦C, to what maximum pressure (according to her pressure gauge) should she fill her tires this morning? Ariel’s car manual recommends a maximum pressure of 30.psi. (Assume a negligible volume change.)

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  1. Answer:

    29.39 psi

    Explanation:

    Assuming volume change then we can say

    [tex]\frac {P_2}{P_1}=\frac {T_2}{T_1}[/tex] where P and T represent pressure and temperature in Kelvin respectively. Making [tex]P_1[/tex] the subject of the formula then

    [tex]\frac {P_1}=\frac {T_1P_2}{T_2}[/tex]

    14 degrees celcius to kelvin will be 273+14=287 K, this is temperature 1

    20 degrees celcius to Kelvin will be 273+20=293 K this is temperature 2

    Pressure 2 is given as 30 psi

    [tex]\frac {P_1}=\frac {287\times 30}{293}=

    29.385665529010 psi\approx 29.39 psi[/tex]

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