Question

Prior to a trip the pressure in a truck tire was 1.8 atm when the temperature was20°C. When the trip was over the pressure was 1.9 atm. Assuming constant volume,what is the new temperature in Kelvin?

Answer 1

We are given air inside a tire. Since this is a system that is at a constant volume we can use Gay-Lussac's law, which states the following:

`(P_1)/(T_1)=(P_2)/(T_2)`

Now we solve for the second temperature, first by multiplying both sides by T2:

`T_2*(P_1)/(T_1)=P_2`

Now we multiply by T1/P1:

`T_2=T_1*\frac{P_2}{P_1_{}}`

Now we replace the known values:

`T_2=(20^0C)((1.9atm))/(1.8atm)`

The temperature must be in Kelvin, therefore, we use the following conversion factor:

`\begin{gathered} K=C+273.15 \\ K=20+273.15 \\ K=293.15 \end{gathered}`

Replacing in the temperature we get:

`T_2=(293.15K)((1.9atm))/(1.8atm)`

Now we solve the operations:

`T_2=309.4K`

We can use the same conversion factor to go back to centigrades:

`\begin{gathered} C=K-273.15 \\ C=309.4-273.15 \\ C=36.25 \end{gathered}`

Therefore, the final temperature is 36.25°C.