Question

The pressure in an automobile tire is 198 kPa at 25°C. At the end of a trip on a hot sunny day, the pressure has risen to 225 kPa. What is the temperature of the air in the tire? (Assume that volume and number of moles has not changed.)

Answer 1

The new temperature in the tire is `"339 K"`.

Explanation:

This is an example of Gay-Lussac's law, which states that the pressure of a given amount of gas held at constant volume is directly proportional to the Kelvin temperature. This means that if the volume increases, so does the temperature, and vice versa.

The equation for this gas law is:

`P_1/T_1=P_2/T_2`

Known

`P_1="198 kPa"`

`T_1="25"^@"C" + 273.15 ="298 K"` `larr` Temp. must be in Kelvins

`P_2="225 kPa"`

Unknown

`T_2`

Solution

Rearrange the equation to isolate `T_2`. Plug in the known values and solve.

`T_2=(T_1P_2)/P_1`

`T_2=(298"K"xx225color(red)cancel(color(black)("kPa")))/(198color(red)cancel(color(black)("kPa")))="339 K"`

`T_2` in `""^@"C"` `=` `"339 K"-273.15="65.9"^@"C"`