Solving Gauge Pressure: Automobile Tire at 20C and 50C

[ch3570r]

"An automobile tire is filled to a gauge pressure of 200 kPa when its temperature is 20C. (Gauge pressure is the difference between the actual pressure and atmostpheric pressure.) After the car has been driven at high speeds, the tires temperature increases to 50C. Assuming that the volume of the tire does not change, and that air behaves as an ideal gas, find the gauge pressure of the air in the tire."

I will use (p2v2/t2)=(p1V1/t1)

(pressure one) p1 = 200kPa
(pressure two) p2 = ?
(volume one) v1 = 1 (because its a constant)
(volume two) v2 = 1 (again, constant)
(temperature one) t1 = 20C = 293 K
(temperature two) t2 = 50K = 323 K

I solve for p2, but i get 220, not 230 as the book says. It might have something to due with the comment in the question about gauge pressure. Anyone see the problem?

 

[geoffjb]

"An automobile tire is filled to a gauge pressure of 200 kPa when its temperature is 20C. (Gauge pressure is the difference between the actual pressure and atmostpheric pressure.) After the car has been driven at high speeds, the tires temperature increases to 50C. Assuming that the volume of the tire does not change, and that air behaves as an ideal gas, find the gauge pressure of the air in the tire."

I will use (p2v2/t2)=(p1V1/t1)

(pressure one) p1 = 200kPa
(pressure two) p2 = ?
(volume one) v1 = 1 (because its a constant)
(volume two) v2 = 1 (again, constant)
(temperature one) t1 = 20C = 293 K
(temperature two) t2 = 50K = 323 K

I solve for p2, but i get 220, not 230 as the book says. It might have something to due with the comment in the question about gauge pressure. Anyone see the problem?

You're correct in that you must use the actual pressure, not the gauge pressure. Re-try your calculation.