Question

The gauge pressure in your car tires is 2.50×105N/m2 at a temperature of 35.0ºC when you drive it onto a ferry boat to Alaska. What is their gauge pressure later, when their temperature has dropped to –40.0ºC

Answer 1

Answer:

1.645 x 10^5 Pa

Explanation:

Let Po be the atmospheric pressure. Po = 1.01 x 10^5 Pa

P1 = 2.5 x 10^5 + Po = 2.5 x 10^5 + 1.01 x 10^5 = 3.51 x 10^5 Pa

T1 = 35 degree C = 35 + 273 = 308 k

T2 = - 40 degree C = - 40 + 273 = 233 k

Let the gauge pressure be P

So, P2 = P + Po

use

P1 / T1 = P2 / T2

3.51 x 10^5 / 308 = P2 / 233

P2 = 2.655 x 10^5

P + Po = 2.655 x 10^5

P = 2.655 x 10^5 - 1.01 x 10^5 = 1.645 x 10^5 Pa

Thus, the gauge pressure is 1.645 x 10^5 Pa.