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29 June, 03:37

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

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  1. 29 June, 04:37
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    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.
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