Question

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.)

Answer 1

Answer:

29.39 psi

Explanation:

Assuming volume change then we can say

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

$\frac {P_1}=\frac {T_1P_2}{T_2}$

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

$\frac {P_1}=\frac {287\times 30}{293}=29.385665529010 psi\approx 29.39 psi$