Question

The gage pressure of an automobile tire is measured to be 210kPa before a trip and 220kPa after the trip at a location where the atmospheric pressure is 95kPa. Assuming the volume of the tire remains constant and the air temperature before the trip is 25o C, determine the air temperature in the tire after the trip. (

Answer 1

To calculate the air temperature in the tire after the trip, you use the combined gas law with the assumption that volume is constant and solve for the final temperature in Kelvin, then convert it to Celsius.

Step-by-step explanation:

To determine the air temperature in the tire after the trip, the combined gas law can be used. It relates the pressure, volume, and temperature of a gas. Since the volume of the tire is assumed to be constant, the relationship between pressure and temperature can be simplified using the formula P1/T1 = P2/T2, where P1 and P2 are the initial and final pressures, and T1 and T2 are the initial and final temperatures in Kelvin, respectively.

First, convert the celsius temperature to Kelvin by adding 273.15. The initial temperature is 25° C or 298.15 K. Use the given gauge pressures for P1 and P2 and add atmospheric pressure to get absolute pressures: P1 = 305 kPa (210 kPa + 95 kPa) and P2 = 315 kPa (220 kPa + 95 kPa).

Applying the formula: (305 kPa)/(298.15 K) = (315 kPa)/T2, solve for T2. The result is the final temperature in Kelvin, and it can be converted back to Celsius by subtracting 273.15.

Through this calculation, we could find the air temperature in the tire after the trip.

Answer 2

`T_(f) = 312.348\,K\,(39.198\,K)`

Step-by-step explanation:

Let assume that gas inside the automobile tire behaves as an ideal gas. Due to the absence of leakages, the number of moles remains constant during the trip. Air temperature can be found by using the following relation:

`(P_(o))/(T_(o))=(P_(f))/(T_(f))`

Final temperature is cleared with the expression:

`T_(f) = (P_(f))/(P_(o))\cdot T_(o)`

`T_(f) = (220\,kPa)/(210\,kPa)\cdot (298.15\,K)`

`T_(f) = 312.348\,K\,(39.198\,K)`