Question

The gauge pressure in your car tires is 2.50 x 105 N/m^2 at a temperature of 35.0ºC when you drive it onto a ship in Los Angeles to be sent to Alaska. What is their gauge pressure on a night in Alaska when their temperature has dropped to -40.0ºC? Assume the tires have not gained or lost any air

Answer 1

the new ppresure 1.89 10⁵ Pa

Step-by-step explanation:

In this case we assume that the air is compiled as an ideal gas, which is described by the expression

P V = nR T

Where P is the pressure and T is the absolute temperature, let's write this expression for the two points that tell us

P1 = (nR / V) T1

P1 / T1 = nR / V

P2 = (nR / V) T2

P2 / T2 = nR / V

With the constant on the right side is the same we can match the two equations

P1 / T1 = P2 / T2

Let's take the tempera to absolute

T1 = 35.0 + 273.15

T1 = 308.15K

T2 = -40.0 + 273.15

T2 = 233.15K

Let's clear and calculate the pressure (P2)

P2 = P1 T2 / T1

P2 = 2.50 10⁵ 233.15 / 308.15

P2 = 1.89 10⁵ Pa