Question

A car tire was inflated to a gauge pressure of 22.0 psi on a cold day when the temperature was -3degree C. What pressure will be found on the tire gauge on a warmer day when the temperature is 31degreeC? Assume an average atmospheric pressure at sea level and that the tire does not leak or expand. [ ]psi What if the tire had expanded by 2.00 %? What would the gauge read on the warmer day? [ ]psi

Answer 1

(1) Tire does not leak or expand. Hence, the volume remains constant.

$T=273-3=270 \quad K$

$T'=273+31=304 \quad K$

$P' = \frac {T'}{T} \times P=\frac {304 \quad K}{270 \quad } \times 22.0 \quad psi=24.7 \quad psi.$

Here, P and P' are initial and final pressures and T and T' are the initial and final temperatures.

Hence, the pressure on warmer day without leakage or expansion is 24.7 psi.

(2) The tire expands by 2%

Hence, $V"=\frac {102}{100}V$

Here V and V" are initial and final volumes.

$P"=\frac {T"}{T} \times \frac {V}{V"} \times P=\frac {304 \quad K}{270 \quad K} \times \frac {100 \quad V}{102 \quad V} \times 22.0 \quad psi=24.3 \quad psi$

Hence, the pressure on warmet day with expansion is 24.3 psi.