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.

 

[kyle8921]

I would first like to clarify that the term "gauge pressure" refers to the pressure measured by a gauge, which is the difference between the actual pressure and atmospheric pressure. In this case, the given gauge pressure of 200 kPa is already the difference between the actual pressure and atmospheric pressure. Therefore, we do not need to adjust for atmospheric pressure in our calculations.

Using the ideal gas law, we can solve for the new gauge pressure (p2) using the given values:

(p1V1)/t1 = (p2V2)/t2

Substituting our values:

(200 kPa)(1 L)/(293 K) = (p2)(1 L)/(323 K)

Solving for p2, we get:

p2 = (200 kPa)(323 K)/(293 K) = 220 kPa

Therefore, the gauge pressure of the air in the tire at 50C is 220 kPa, not 230 kPa as stated in the question. It is possible that the book made a mistake or used a different method to calculate the gauge pressure. As scientists, it is important to always double check our calculations and results, and to also consider potential sources of error.