Question

What final temperature (°C) is required for the pressure inside an automobile tire to increase from 2.15 atm at 0°C to 2.37 atm, assuming the volume remains constant?

Answer 1

So, in this problem you'll need to use one of the smaller parts of the ideal gas law dealing with Temperature and Pressure called Charles' law. This basically says that when volume and amount of gas are constant, then pressure is directly proportional to Kelvin temperature. For the purposes of this problem, that means:

`P_1/T_1 = P_2/T_2`

So the calculations are really not that hard. The only trap to avoid is to make sure you convert your temperature to Kelvin. This is pretty easy to do; just add 273.15 to your degree temperature. Hence, you'll have your initial temperature as `273.15 K` as opposed to `0^oC`

Now, let's just plug in & solve:

`2.15/273.15 = 2.37/T_2`

`T_2 = 2.37/(2.15/273.15) = 301 K`

And that's about it. Now if you were asked for the final temperature in celcius, all you'd need to do is subtract 273.15. This leaves you with:

`301-273.15 = 28.0^oC`

Hope that helped :)