Question

In the morning, when the temperature is 286 K , a bicyclist finds that the gauge pressure in his tires is 404 kPa . That afternoon she finds that the pressure in the tires has increased to 422 kPa .

Part A What is the afternoon temperature?

Answer 1

The answer is 298.74K

Step-by-step explanation:

Ideal gas formula is following:

`P*V=n*R*T`

We are assuming that, except temperature and pressure, all other variables are constant. So if we define morning temperature and pressure as:

`T_(0)=286K\\P_(0)=404kPa`

Then if we write the same formula for afternoon time the equation will be:

`P_(1)*V=n*R*T_(1)\\1.045*P_(0)*V=n*R*T_(1)`

Then we find out that the must be correlation between morning and afternoon temperature as following:

`T_(1)=1.045*T_(0)\\T_(1)=1.045*286\\T_(1)=298.74K`