An automobile tire has a maximum rating of 38 psi (gauge pressure). The tire is

Question

An automobile tire has a maximum rating of 38 psi (gauge pressure). The tire is inflated (while cold) to a volume of 11.8L and a gauge pressure of 36.0 psi at a temperature of 12.0 C. Driving on a hot day, the tire warms to 65 degrees Celsius and its volume expands to 12.2L. Does the pressure in the tire exceed its maximum rating ? An automobile tire has a maximum rating of 38 psi (gauge pressure). The tire is inflated (while cold) to a volume of 11.8L and a gauge pressure of 36.0 psi at a temperature of 12.0 C. Driving on a hot day, the tire warms to 65 degrees Celsius and its volume expands to 12.2L. Does the pressure in the tire exceed its maximum rating ?

Explanation / Answer

First calculate the P1 by add the atmospheric pressure as follows:

P1 = 36 psig + 14.7 = 50.7 psi

And V1 = 11.8 L , T1 = 12 + 273 = 285 K
P2 = ? , V2 = 12.2L , T2 = 65 C + 273 = 338K

Gas equation is following:

P1 V1 T2 = P2 V2 T1

P2 = P1 V1 T2/ V2 T1

P2= (50.7 psi)(11.8 L) (338K) / (12.2L)(285K)

P2 = (50.7 psi)(11.8 L) (338K) / (12.2L)(285K)


P2 = 58.16 psi

Now calculate the final pressure of tire=

58.16 psi - 14.7 = 43.46 psig

Yes the tire exceeding its maximum pressure rating.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.